Electromagnetic flowmeter

ABSTRACT

When a plane (PLN) which includes electrodes ( 2   a   , 2   b ) and is perpendicular to the direction of an axis (PAX) of a measuring pipe ( 1 ) is defined as a boundary in the measuring pipe ( 1 ), an exciting coil ( 3 ) applies asymmetrical magnetic fields to a fluid to be measured, which flows through the measuring pipe ( 1 ), on both sides of the plane (PLN) serving as the boundary in the measuring pipe ( 1 ). A signal conversion unit ( 5 ) obtains the phase difference between an exciting current supplied to the exciting coil ( 3 ) and an interelectrode electromotive force detected by the electrodes ( 2   a   , 2   b ). A flow rate output unit ( 6 ) calculates the flow rate of the fluid on the basis of the phase difference obtained by the signal conversion unit ( 5 ).

The present patent application is a non-provisional National Stageapplication of International Application No. PCT/JP02/09679, filed Sep.20, 2002.

BACKGROUND OF THE INVENTION

The present invention relates to an electromagnetic flowmeter whichmeasures the flow rate of a fluid to be measured, which flows through ameasuring pipe and, more particularly, to an exciting method and signalprocessing method capable of realizing accurate flow rate measurement.

An electromagnetic flowmeter measures the flow rate of a conductivefluid to be measured, which flows through a measuring pipe, byconverting the flow rate into an electrical signal by usingelectromagnetic induction. FIG. 25 shows the arrangement of aconventional electromagnetic flowmeter. This electromagnetic flowmeterhas a measuring pipe 11, a pair of electrodes 12 a and 12 b, an excitingcoil 13, a signal conversion unit 15, and a flow rate output unit 16. Afluid to be measured flows through the measuring pipe 11. The pair ofelectrodes 12 a and 12 b oppose each other in the measuring pipe 11 tobe perpendicular to both the magnetic field applied to the fluid to bemeasured and an axis PAX of the measuring pipe 11 and also come intocontact with the fluid to be measured. The electrodes 12 a and 12 bdetect an electromotive force generated by the magnetic field and theflow of the fluid to be measured. The exciting coil 13 applies, to thefluid to be measured, a magnetic field perpendicular to both themeasuring pipe axis PAX and an electrode axis EAX that connects theelectrodes 12 a and 12 b. The signal conversion unit 15 detects theelectromotive force between the electrodes 12 a and 12 b. The flow rateoutput unit 16 calculates the flow rate of the fluid to be measured onthe basis of the interelectrode electromotive force detected by thesignal conversion unit 15.

In the electromagnetic flowmeter shown in FIG. 25, a plane PLN whichincludes the electrodes 12 a and 12 b and is perpendicular to thedirection of the measuring pipe axis PAX is defined as a boundary in themeasuring pipe 11. At this time, symmetrical magnetic fields are appliedto the fluid to be measured on both sides of the plane PLN, i.e., theboundary in the measuring pipe 11. The exciting coil 13 can be excitedby a sine wave exciting method capable of high-frequency excitation or arectangular wave exciting method which is not affected byelectromagnetic induction noise.

The sine wave exciting method that uses a sine wave as an excitingcurrent for an exciting coil is readily affected by commercial frequencynoise. However, this problem can be solved by a high-frequency excitingmethod which uses an exciting current having a higher frequency. Thehigh-frequency exciting method is resistant to 1/f noise such aselectrochemical noise or spike noise. In addition, this method canimprove the response (a characteristic which makes a flow rate signalquickly follow a change in flow rate).

However, the conventional sine wave exciting method is readily affectedby in-phase component noise. An example of in-phase component noise is ashift of the amplitude of a magnetic field applied to a fluid to bemeasured. In the conventional electromagnetic flowmeter, when theamplitude of the exciting current supplied to the exciting coil varies(shifts) due to a fluctuation in power supply voltage, and the amplitudeof the magnetic field applied to the fluid to be measured shifts, theamplitude of the interelectrode electromotive force changes, resultingin a flow rate measurement error due to the influence of shift. Suchin-phase component noise cannot be removed even by the high-frequencyexciting method.

To the contrary, the rectangular wave exciting method that uses arectangular wave as an exciting current to be supplied to an excitingcoil is resistant to in-phase component noise. In the rectangular waveexciting method, however, the interelectrode electromotive force isdetected when a change in magnetic field becomes zero. When the excitingcurrent has a high frequency, the detector must have high performance.Additionally, in the rectangular wave exciting method, when the excitingcurrent has a high frequency, effects of the impedance of the excitingcoil, the exciting current response, the magnetic field response, and anovercurrent loss in the core of the exciting coil or measuring pipecannot be neglected. It is difficult to maintain rectangular waveexcitation. As a result, in the rectangular wave exciting method,high-frequency excitation is difficult, and an increase in response to achange in flow rate or removal of 1/f noise cannot be realized.

DISCLOSURE OF INVENTION

The present invention has been made to solve the above-describedproblems, and has as its object to provide an electromagnetic flowmeterwhich can remove in-phase component noise and correct any flow ratemeasurement error and also realize high-frequency excitation.

An electromagnetic flowmeter according to the present inventioncomprises a measuring pipe through which a fluid to be measured flows,an electrode which is arranged in the measuring pipe and detects anelectromotive force generated by a magnetic field applied to the fluidand flow of the fluid, an asymmetrical exciting unit which appliesasymmetrical magnetic fields to the fluid on both sides of a planeserving as a boundary in the measuring pipe, the plane including theelectrode, being perpendicular to an axial direction of the measuringpipe, and being defined as the boundary in the measuring pipe, a signalconversion unit which obtains, from an electromotive force detected bythe electrode, an asymmetrical exciting characteristic parameter whichdepends on a flow rate of the fluid and does not depend on a flow ratemeasurement error, and a flow rate output unit which calculates the flowrate of the fluid for which the flow rate measurement error has beencorrected on the basis of the asymmetrical exciting characteristicparameter. As the basic technical idea of the present invention,asymmetrical magnetic fields are applied to the fluid on both sides ofthe boundary in the measuring pipe, i.e., the electrode axis whichconnects the electrodes to generate a phase difference between the input(exciting current) and the output (electromotive force). A flow ratemeasurement error due to the shift of the magnetic field state iscorrected on the basis of the mechanism of the phase difference. Morespecifically, when asymmetrical magnetic fields (magnetic fields whichperiodically change) are applied to the fluid on both sides of the planeserving as the boundary in the measuring pipe, an electromotive forcecaused not by the flow velocity but by the change in magnetic field(magnetic flux) is generated in the electrode in addition to theelectromotive force caused by the movement of the fluid, i.e., the flowvelocity. The phase difference between the electromotive forces has apredetermined relationship. Hence, when the phase difference between thephase of the exciting current and the electromotive force generated inthe electrode is taken into consideration, in-phase component can beremoved. Hence, the rectangular wave exciting method need not be used,and the sine wave exciting method can be used.

In an arrangement of the electromagnetic flowmeter according to thepresent invention, the asymmetrical exciting unit comprises an excitingcoil which is arranged at a position separated from the plane by anoffset distance, and a power supply unit which supplies an excitingcurrent to the exciting coil. When the exciting coil is arranged at theposition separated from the plane by the offset distance, asymmetricalmagnetic fields can be applied to the fluid to be measured on both sidesof the plane serving as the boundary in the measuring pipe.

In an arrangement of the electromagnetic flowmeter according to thepresent invention, the signal conversion unit obtains, as theasymmetrical exciting characteristic parameter, a phase differencebetween an exciting current supplied to an exciting coil of theasymmetrical exciting unit and the electromotive force detected by theelectrode, and the flow rate output unit calculates the flow rate of thefluid on the basis of the phase difference obtained by the signalconversion unit. When asymmetrical magnetic fields are applied to thefluid to be measured on both sides of the plane serving as the boundaryin the measuring pipe by using at least one exciting coil, the phasedifference between the exciting current and the electromotive forcedetected by the electrode is constant unless the flow rate of the fluidto be measured changes. In other words, when the flow rate of the fluidchanges, the phase difference between the exciting current and theelectromotive force changes. For this reason, the flow rate of the fluidto be measured can be calculated from the phase difference between theexciting current and the electromotive force.

An electromagnetic flowmeter according to the present inventioncomprises a measuring pipe through which a fluid to be measured flows,an electrode which is arranged in the measuring pipe and detects anelectromotive force generated by a magnetic field applied to the fluidand flow of the fluid, an exciting coil which is arranged at a positionseparated from a plane by an offset distance and applies asymmetricalmagnetic fields to the fluid on both sides of the plane serving as aboundary in the measuring pipe, the plane including the electrode, beingperpendicular to an axial direction of the measuring pipe, and beingdefined as the boundary in the measuring pipe, a power supply unit whichsupplies an exciting current to the exciting coil, a signal conversionunit which obtains a phase difference between the exciting current andan electromotive force detected by the electrode, and a flow rate outputunit which calculates a flow rate of the fluid on the basis of the phasedifference obtained by the signal conversion unit.

In an arrangement of the electromagnetic flowmeter according to thepresent invention, the asymmetrical exciting unit comprises a firstexciting coil which is arranged at a position separated from the planeby an offset distance, a second exciting coil which is arranged at aposition different from that of the first exciting coil, and a powersupply unit which supplies exciting currents having the same phase tothe first exciting coil and the second exciting coil, and in a magneticfield generated from the first exciting coil and a magnetic fieldgenerated from the second exciting coil, magnetic field components whichare perpendicular to both of an axial direction of the electrode and theaxial direction of the measuring pipe have the same phase and differentamplitudes on the axis of the electrode. When the first exciting coil isarranged at the position separated from the plane by the offsetdistance, and the second exciting coil is arranged at the positiondifferent from that of the first exciting coil, asymmetrical magneticfields can be applied to the fluid to be measured on both sides of theplane serving as the boundary in the measuring pipe. To generate theasymmetrical magnetic fields, a method of arranging the first excitingcoil and second exciting coil asymmetrically with respect to the planeor a method of supplying exciting currents having different amplitudesto the first exciting coil and second exciting coil can be used.

An electromagnetic flowmeter according to the present inventioncomprises a measuring, pipe through which a fluid to be measured flows,an electrode which is arranged in the measuring pipe and detects anelectromotive force generated by a magnetic field applied to the fluidand flow of the fluid, a first exciting coil which is arranged at aposition separated from a plane by an offset distance, the planeincluding the electrode, being perpendicular to an axial direction ofthe measuring pipe, and being defined as the boundary in the measuringpipe, a second exciting coil which is arranged at a position differentfrom that of the first exciting coil, a power supply unit which suppliesexciting currents having the same phase to the first exciting coil andthe second exciting coil, a signal conversion unit which obtains a phasedifference between the exciting current and an electromotive forcedetected by the electrode, and a flow rate output unit which calculatesa flow rate of the fluid on the basis of the phase difference obtainedby the signal conversion unit, wherein in a magnetic field generatedfrom the first exciting coil and a magnetic field generated from thesecond exciting coil, magnetic field components which are perpendicularto both of an axial direction of the electrode and the axial directionof the measuring pipe have the same phase and different amplitudes onthe axis of the electrode. When asymmetrical magnetic fields are appliedto the fluid to be measured on both sides of the plane serving as theboundary in the measuring pipe by using two exciting coils, and excitingcurrents having the same phase are supplied to the first exciting coiland second exciting coil, the phase difference between the excitingcurrent and the electromotive force detected by the electrode isconstant unless the flow rate of the fluid to be measured changes. Inother words, when the flow rate of the fluid changes, the phasedifference between the exciting current and the electromotive forcechanges. For this reason, the flow rate of the fluid to be measured canbe calculated from the phase difference between the exciting current andthe electromotive force.

In an arrangement of the electromagnetic flowmeter according to thepresent invention, on the basis of the phase difference φ obtained bythe signal conversion unit, the flow rate output unit calculates theflow rate of the fluid by α1×tan(π/2−φ) (α1 is a coefficient). In thiscase, α1 is a predetermined coefficient.

In an arrangement of the electromagnetic flowmeter according to thepresent invention, the asymmetrical exciting unit comprises a firstexciting coil which is arranged at a position separated from the planeby an offset distance, a second exciting coil which is arranged at aposition different from that of the first exciting coil, and a powersupply unit which supplies exciting currents to the first exciting coiland the second exciting coil while changing a phase difference betweenthe exciting current supplied to the first exciting coil and theexciting current supplied to the second exciting coil, and in a magneticfield generated from the first exciting coil and a magnetic fieldgenerated from the second exciting coil, magnetic field components whichare perpendicular to both of an axial direction of the electrode and theaxial direction of the measuring pipe have the same amplitude on theaxis of the electrode, and the phase difference between the magneticfield component of the first exciting coil and the magnetic fieldcomponent of the second exciting coil changes. That the phase differencebetween the magnetic fields of two exciting coils changes means morespecifically that the phase difference takes at least two differentstates, i.e., the phase difference takes at least two values. The phasedifference between the magnetic field components can be obtained fromthe phase difference between the exciting currents supplied to the firstand second exciting coils.

In an arrangement of the electromagnetic flowmeter according to thepresent invention, the signal conversion unit obtains an amplitude ofthe electromotive force detected by the electrode for each of at leasttwo states with different phase differences between the excitingcurrents supplied to the two exciting coils of the asymmetrical excitingunit and obtains a ratio of the amplitudes as the asymmetrical excitingcharacteristic parameter, and the flow rate output unit calculates theflow rate of the fluid on the basis of the ratio of the amplitudesobtained by the signal conversion unit. When asymmetrical magneticfields are applied to the fluid to be measured on both sides of theplane serving as the boundary in the measuring pipe by using twoexciting coils, and the magnetic field component generated from thefirst exciting coil and that generated from the second exciting coilhave the same amplitude, the amplitude ratio of the electromotive forcedetected by the electrode does not change even when the amplitude of themagnetic field changes. For this reason, the flow rate of the fluid tobe measured can be calculated from the amplitude ratio of theelectromotive force.

An electromagnetic flowmeter according to the present inventioncomprises a measuring pipe through which a fluid to be measured flows,an electrode which is arranged in the measuring pipe and detects anelectromotive force generated by a magnetic field applied to the fluidand flow of the fluid, a first exciting coil which is arranged at aposition separated from a plane by an offset distance, the planeincluding the electrode being perpendicular to an axial direction of themeasuring pipe, and being defined as the boundary in the measuring pipe,a second exciting coil which is arranged at a position different fromthat of the first exciting coil, a power supply unit which suppliesexciting currents to the first exciting coil and the second excitingcoil while changing a phase difference between the exciting currentsupplied to the first exciting coil and the exciting current supplied tothe second exciting coil, a signal conversion unit which obtains anamplitude of the electromotive force detected by the electrode for eachof at least two states with different phase differences and obtains aratio of the amplitudes, and a flow rate output unit which calculates aflow rate of the fluid on the basis of the ratio of the amplitudesobtained by the signal conversion unit, wherein in a magnetic fieldgenerated from the first exciting coil and a magnetic field generatedfrom the second exciting coil, magnetic field components which areperpendicular to both of an axial direction of the electrode and theaxial direction of the measuring pipe have the same amplitude on theaxis of the electrode, and the phase difference between the magneticfield component of the first exciting coil and the magnetic fieldcomponent of the second exciting coil takes at least two values.

In an arrangement of the electromagnetic flowmeter according to thepresent invention, when the phase difference between the excitingcurrent supplied to the first exciting coil and the exciting currentsupplied to the second exciting coil takes two values 2χ and 2ψ (χ and ψare different real numbers), the flow rate output unit calculates, onthe basis of a ratio R of the amplitudes obtained by the signalconversion unit, the flow rate of the fluid by α2×{(R sin ψ−sin χ)/(Rcos ψ−cos χ) (α2 is a coefficient). In this case, α2 is a predeterminedcoefficient.

In an arrangement of the electromagnetic flowmeter according to thepresent invention, the asymmetrical exciting unit comprises a firstexciting coil which is arranged at a position separated from the planeby an offset distance, a second exciting coil which is arranged at aposition different from that of the first exciting coil, and a powersupply unit which supplies exciting currents to the first exciting coiland the second exciting coil while continuously switching a phasedifference between the exciting current supplied to the first excitingcoil and the exciting current supplied to the second exciting coil, andin a magnetic field generated from the first exciting coil and amagnetic field generated from the second exciting coil, magnetic fieldcomponents which are perpendicular to both of an axial direction of theelectrode and the axial direction of the measuring pipe have the sameamplitude on the axis of the electrode, and the phase difference betweenthe magnetic field component of the first exciting coil and the magneticfield component of the second exciting coil continuously switches.

In an arrangement of the electromagnetic flowmeter according to thepresent invention, the signal conversion unit obtains an amplitude ofthe electromotive force detected by the electrode for each of aplurality of states with different phase differences between theexciting currents supplied to the two exciting coils of the asymmetricalexciting unit and obtains, as the asymmetrical exciting characteristicparameter, the phase difference for which the amplitude has apredetermined value, and the flow rate output unit calculates the flowrate of the fluid on the basis of the phase difference obtained by thesignal conversion unit. When asymmetrical magnetic fields are applied tothe fluid to be measured on both sides of the plane serving as theboundary in the measuring pipe by using two exciting coils, and themagnetic field component generated from the first exciting coil and thatgenerated from the second exciting coil have the same amplitude, thephase difference between the exciting currents for which the amplitudeof the electromotive force detected by the electrode has a predeterminedvalue does not depend on the amplitude of the magnetic field. For thisreason, the flow rate of the fluid to be measured can be calculated fromthe phase difference between the exciting currents for which theamplitude of the electromotive force has a predetermined value.

An electromagnetic flowmeter according to the present inventioncomprises a measuring pipe through which a fluid to be measured flows,an electrode which is arranged in the measuring pipe and detects anelectromotive force generated by a magnetic field applied to the fluidand flow of the fluid, a first exciting coil which is arranged at aposition separated from a plane by an offset distance, the planeincluding the electrode, being perpendicular to an axial direction ofthe measuring pipe, and being defined as the boundary in the measuringpipe, a second exciting coil which is arranged at a position differentfrom that of the first exciting coil, a power supply unit which suppliesexciting currents to the first exciting coil and the second excitingcoil while continuously switching a phase difference between theexciting current supplied to the first exciting coil and the excitingcurrent supplied to the second exciting coil, a signal conversion unitwhich obtains an amplitude of the electromotive force detected by theelectrode for each of a plurality of states with different phasedifferences and obtains the phase difference for which the amplitude hasa predetermined value, and a flow rate output unit which calculates aflow rate of the fluid on the basis of the phase difference obtained bythe signal conversion unit, wherein in a magnetic field generated fromthe first exciting coil and a magnetic field generated from the secondexciting coil, magnetic field components which are perpendicular to bothof an axial direction of the electrode and the axial direction of themeasuring pipe have the same amplitude on the axis of the electrode, andthe phase difference between the magnetic field component of the firstexciting coil and the magnetic field component of the second excitingcoil continuously switches.

In an arrangement of the electromagnetic flowmeter according to thepresent invention, on the basis of the phase difference θ2 obtained bythe signal conversion unit, the flow rate output unit calculates theflow rate of the fluid by α3×tan(θ2/2) (α3 is a coefficient). In thiscase, α3 is a predetermined coefficient.

In an arrangement of the electromagnetic flowmeter according to thepresent invention, the asymmetrical exciting unit comprises a firstexciting coil which is arranged at a position separated from the planeby an offset distance, a second exciting coil which is arranged at aposition different from that of the first exciting coil, and a powersupply unit which supplies exciting currents having the same frequencyand a predetermined phase difference to the first exciting coil and thesecond exciting coil while changing the frequency, and in a magneticfield generated from the first exciting coil and a magnetic fieldgenerated from the second exciting coil, magnetic field components whichare perpendicular to both of an axial direction of the electrode and theaxial direction of the measuring pipe have the same amplitude, samefrequency, and the predetermined phase difference on the axis of theelectrode, and the frequency of the magnetic field component switchesbetween at least two values.

In an arrangement of the electromagnetic flowmeter according to thepresent invention, the signal conversion unit obtains an amplitude ofthe electromotive force detected by the electrode for each of at leasttwo states in which the frequency of the exciting currents supplied tothe two exciting coils of the asymmetrical exciting unit switches andobtains a ratio of the amplitudes as the asymmetrical excitingcharacteristic parameter and the flow rate output unit calculates theflow rate of the fluid on the basis of the ratio of the amplitudesobtained by the signal conversion unit.

An electromagnetic flowmeter according to the present inventioncomprises a measuring pipe through which a fluid to be measured flows,an electrode which is arranged in the measuring pipe and detects anelectromotive force generated by a magnetic field applied to the fluidand flow of the fluid, a first exciting coil which is arranged at aposition separated from a plane by an offset distance, the planeincluding the electrode, being perpendicular to an axial direction ofthe measuring pipe, and being defined as the boundary in the measuringpipe, a second exciting coil which is arranged at a position differentfrom that of the first exciting coil, a power supply unit which suppliesexciting currents having the same frequency and a predetermined phasedifference to the firs t exciting coil and the second exciting coilwhile changing the frequency a signal conversion unit which obtains anamplitude of the electromotive force detected by the electrode for eachof at least two states with different frequencies and obtains a ratio ofthe amplitudes, and a flow rate output unit which calculates a flow rateof the fluid on the basis of the ratio of the amplitudes obtained by thesignal conversion unit, wherein in a magnetic field generated from thefirst exciting coil and a magnetic field generated from the secondexciting coil, magnetic field components which are perpendicular to bothof an axial direction of the electrode and the axial direction of themeasuring pipe have the same amplitude, same frequency, and thepredetermined phase difference on the axis of the electrode, and thefrequency of the magnetic field component switches between at least twovalues, i.e., takes at least two different frequencies.

In an arrangement of the electromagnetic flowmeter according to thepresent invention, when the frequency of the exciting currents suppliedto the first and second exciting coils switches between two values ω1and ω2, the flow rate output unit calculates, on the basis of a ratioRor of the amplitudes obtained by the signal conversion unit, the flowrate of the fluid by α4×{(Rorω2−ω1)sin(θ2/2)}/{(1−Ror)cos(θ2/2)} (α4 isa coefficient). In this case, α4 is a predetermined coefficient.

In an arrangement of the electromagnetic flowmeter according to thepresent invention, when the frequency of the exciting currents suppliedto the first and second exciting coils switches between two values ω1and ω2, the flow rate output unit calculates, on the basis of a ratioRvx of real axis components of the amplitudes obtained by the signalconversion unit, the flow rate of the fluid byα4×{(Rvxω2−ω1)sin(θ2)}/[(1−Rvx)(1+cos(θ2)}] (α4 is a coefficient).

In an arrangement of the electromagnetic flowmeter according to thepresent invention, when the frequency of the exciting currents suppliedto the first and second exciting coils switches between two values ω1and ω2, the flow rate output unit calculates, on the basis of a ratioRvy of imaginary axis components of the amplitudes obtained by thesignal conversion unit, the flow rate of the fluid byα4×[(Rvyω2−ω1){1−cos(θ2)}]/{(1−Rvy)sin(θ2)} (α4 is a coefficient).

In an arrangement of the electromagnetic flowmeter according to thepresent invention, the asymmetrical exciting unit comprises a firstexciting coil which is arranged at a position separated from the planeby an offset distance, a second exciting coil which is arranged at aposition different from that of the first exciting coil, and a powersupply unit which supplies exciting currents having the same frequencyand a predetermined phase difference to the first exciting coil and thesecond exciting coil while continuously switching the frequency, and ina magnetic field generated from the first exciting coil and a magneticfield generated from the second exciting coil, magnetic field componentswhich are perpendicular to both of an axial direction of the electrodeand the axial direction of the measuring pipe have the same amplitude,same frequency, and the predetermined phase difference on the axis ofthe electrode, and the frequency of the magnetic field componentcontinuously switches.

In an arrangement of the electromagnetic flowmeter according to thepresent invention, the signal conversion unit obtains an amplitude ofthe electromotive force detected by the electrode for each of aplurality of states in which the frequency of the exciting currentssupplied to the two exciting coils of the asymmetrical exciting unitswitches and obtains, as the asymmetrical exciting characteristicparameter, the frequency of the exciting current for which the amplitudehas a predetermined value, and the flow rate output unit calculates theflow rate of the fluid on the basis of the frequency obtained by thesignal conversion unit.

An electromagnetic flowmeter according to the present inventioncomprises a measuring pipe through which a fluid to be measured flows,an electrode which is arranged in the measuring pipe and detects anelectromotive force generated by a magnetic field applied to the fluidand flow of the fluid, a first exciting coil which is arranged at aposition separated from a plane by an offset distance, the planeincluding the electrode, being perpendicular to an axial direction ofthe measuring pipe, and being defined as the boundary in the measuringpipe, a second exciting coil which is arranged at a position differentfrom that of the first exciting coil, a power supply unit which suppliesexciting currents having the same frequency and a predetermined phasedifference to the first exciting coil and the second exciting coil whilecontinuously switching the frequency, a signal conversion unit whichobtains an amplitude of the electromotive force detected by theelectrode for each of a plurality of states with different frequenciesand obtains the frequency for which the amplitude has a predeterminedvalue, and a flow rate output unit which calculates a flow rate of thefluid on the basis of the frequency obtained by the signal conversionunit, wherein in a magnetic field generated from the first exciting coiland a magnetic field generated from the second exciting coil, magneticfield components which are perpendicular to both of an axial directionof the electrode and the axial direction of the measuring pipe have thesame amplitude, same frequency, and the predetermined phase differenceon the axis of the electrode and the frequency of the magnetic fieldcomponent continuously switches.

In an arrangement of the electromagnetic flowmeter according to thepresent invention, on the basis of the phase difference θ2 between theexciting current supplied to the first exciting coil and the excitingcurrent supplied to the second exciting coil and the frequency ω0obtained by the signal conversion unit, the flow rate output unitcalculates the flow rate of the fluid by α5×ω0 tan(θ2/2) (α5 is acoefficient).

An arrangement of the electromagnetic flowmeter according to the presentinvention uses a sine wave exciting method.

In an arrangement of the electromagnetic flowmeter according to thepresent invention, the number of the electrodes is one.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a block diagram for explaining the basic principle of anelectromagnetic flowmeter according to the present invention;

FIG. 2 is a view showing an eddy current and interelectrodeelectromotive force when the flow rate of a fluid to be measured is 0;

FIG. 3 is a view showing an eddy current and interelectrodeelectromotive force when the flow rate of a fluid to be measured is not0;

FIG. 4 is a graph showing the geometrical relationship between fourcomplex vectors representing the interelectrode electromotive force inthe electromagnetic flowmeter shown in FIG. 1;

FIGS. 5A and 5B are explanatory views for explaining problems in aconventional electromagnetic flowmeter;

FIG. 6 is a block diagram showing the arrangement of an electromagneticflowmeter according to the first embodiment of the present invention;

FIGS. 7A and 7B are graphs showing the principle of flow ratemeasurement with shift correction in the electromagnetic flowmeteraccording to the first embodiment of the present invention;

FIG. 8 is a block diagram showing the arrangement of an electromagneticflowmeter according to the second embodiment of the present invention;

FIGS. 9A and 9B are graphs showing the principle of flow ratemeasurement with shift correction in the electromagnetic flowmeteraccording to the second embodiment of the present invention;

FIG. 10 is a block diagram showing the arrangement of an electromagneticflowmeter according to the third embodiment of the present invention;

FIG. 11 is a block diagram showing the arrangement of an electromagneticflowmeter according to the fourth embodiment of the present invention;

FIG. 12 is a block diagram showing the arrangement of an electromagneticflowmeter according to the fifth embodiment of the present invention;

FIG. 13 is a graph showing the principle of flow rate measurement withshift correction in the electromagnetic flowmeter according to the fifthembodiment of the present invention;

FIG. 14 is a graph showing the principle of flow rate measurement withshift correction in the electromagnetic flowmeter according to the fifthembodiment of the present invention;

FIG. 15 is a graph showing the principle of flow rate measurement withshift correction in the electromagnetic flowmeter according to the fifthembodiment of the present invention;

FIG. 16 is a graph showing the principle of flow rate measurement withshift correction in the electromagnetic flowmeter according to the fifthembodiment of the present invention;

FIG. 17 is a graph showing the principle of flow rate measurement withshift correction in the electromagnetic flowmeter according to the fifthembodiment of the present invention;

FIGS. 18A and 18B are graphs showing the principle of flow ratemeasurement with shift correction in the electromagnetic flowmeteraccording to the fifth embodiment of the present invention;

FIG. 19 is a graph showing the principle of flow rate measurement withshift correction in an electromagnetic flowmeter according to the sixthembodiment of the present invention;

FIGS. 20A and 20B are graphs showing the principle of flow ratemeasurement with shift correction in the electromagnetic flowmeteraccording to the sixth embodiment of the present invention;

FIGS. 21A and 21B are graphs showing the principle of flow ratemeasurement with shift correction in an electromagnetic flowmeteraccording to the seventh embodiment of the present invention;

FIGS. 22A and 22B are graphs showing the principle of flow ratemeasurement with shift correction in an electromagnetic flowmeteraccording to the 10th embodiment of the present invention;

FIG. 23 is a sectional view showing an example of the electrode used inthe electromagnetic flowmeter according to the present invention;

FIG. 24 is a sectional view showing another example of the electrodeused in the electromagnetic flowmeter according to the presentinvention; and

FIG. 25 is a block diagram showing the arrangement of a conventionalelectromagnetic flowmeter.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS Basic Principle

Before a description of the basic principle of the present invention,generally known basic mathematical knowledge will be described. A cosinewave A cos(ωt) and sine wave B sin(ωt), which have the same frequencyand different amplitudes, are synthesized into the following cosinewave. A and B are amplitudes, and ω is an angular frequency.A cos(ωt)+B sin(ωt)=(A ² +B ²)^(1/2) cos(ωt−ε) for ε=tan⁻¹(B/A)  (1)

To analyze the synthesis of equation (1), it is convenient to map thecosine wave A cos(ωt) and sine wave B sin (ωt) onto a complex coordinateplane while plotting the amplitude A of the cosine wave A cos(ωt) alongthe real axis and the amplitude B of the sine wave B sin(ωt) along theimaginary axis. More specifically, on the complex coordinate plane, adistance (A²+B²)^(1/2) from the origin gives the amplitude of thesynthetic wave, and an angle ε=tan⁻¹(B/A) with respect to the real axisgives the phase difference between the synthetic wave and ωt.

In addition, on the complex coordinate plane, the following relationholdsCexp (jε)=C cos(ε)+jC sin(ε)  (2)

Equation (2) is an expression of a complex vector. In equation (2), j isthe imaginary number unit, C is the length of the complex vector, and εis the direction of the complex vector. Hence, to analyze thegeometrical relationship on the complex coordinate plane, it isconvenient to use conversion to a complex vector.

In the following description, to explain a behavior that is exhibited byan interelectrode electromotive force and the manner the presentinvention uses the behavior, mapping to the complex coordinate plane andgeometrical analysis using a complex vector are employed.

First, an interelectrode electromotive force which is irrelevant to theflow rate (flow velocity) of a fluid to be measured per unit time willbe described. FIG. 1 is a block diagram for explaining the basicprinciple of an electromagnetic flowmeter according to the presentinvention. This electromagnetic flowmeter comprises a measuring pipe 1,a pair of electrodes 2 a and 2 b, and a first exciting coil 3 a andsecond exciting coil 3 b. A fluid to be measured flows through themeasuring pipe 1. The pair of electrodes 2 a and 2 b oppose each otherin the measuring pipe 1 to be perpendicular to both the magnetic fieldapplied to the fluid to be measured and an axis PAX of the measuringpipe 1 and also come into contact with the fluid to be measured. Theelectrodes 2 a and 2 b detect an electromotive force generated by themagnetic field and the flow of the fluid to be measured. A plane PLNwhich includes the electrodes 2 a and 2 b and is perpendicular to thedirection of the measuring pipe axis PAX is defined as a boundary in themeasuring pipe 1. In this case, the first exciting coil 3 a and secondexciting coil 3 b apply asymmetrical magnetic fields to the fluid to bemeasured on both sides of the plane PLN, i.e., the boundary in themeasuring pipe 1. In this example, the first exciting coil 3 a andsecond exciting coil 3 b are arranged on opposite sides of the planePLN.

Of the magnetic field generated from the first exciting coil 3 a, amagnetic field component (magnetic flux density) B1 which isperpendicular to both an electrode axis EAX that connects the electrodes2 a and 2 b and the measuring pipe axis PAX on the electrode axis EAX,and of the magnetic field generated from the second exciting coil 3 b, amagnetic field component (magnetic flux density) B2 which isperpendicular to both the electrode axis EAX and the measuring pipe axisPAX on the electrode axis EAX are given byB 1=b 1 cos(ω0 t−θ1)  (3)B 2=b 2 cos(ω0 t−θ2)  (4)

In equations (3) and (4), b1 and b2 are the amplitudes, ω0 is theangular frequency, and θ1 and θ2 are the phase differences (phasedelays) from ω0t. The magnetic flux density B1 will be referred to asthe magnetic field B1, and the magnetic flux density B2 will be referredto as the magnetic field B2.

An electromotive force caused by a change in magnetic field is obtainedby a time differential dB/dt of the magnetic field. The magnetic fieldsB1 and B2 generated from the first exciting coil 3 a and second excitingcoil 3 b are differentiated as followsdB 1/dt−b 1ω0 sin(ω0 t−θ1)  (5)dB 2/dt−b 2ω0 sin(ω0 t−θ2)  (6)

When the flow rate of the fluid to be measured is 0, eddy currentsgenerated by the magnetic fields B1 and B2 contain only componentsgenerated by a change in magnetic fields. An eddy current Ia by themagnetic field B1 and eddy current Ib by the magnetic field B2 havedirections as shown in FIG. 2. Hence, in the plane that includes theelectrode axis EAX and measuring pipe axis PAX, an interelectrodeelectromotive force Ea that is generated by a change in magnetic fieldB1 and is irrelevant to the flow rate (flow velocity) and aninterelectrode electromotive force Eb that is generated by a change inmagnetic field B2 and is irrelevant to the flow rate (flow velocity)have opposite directions, as shown in FIG. 2.

At this time, a total interelectrode electromotive force E obtained byadding the interelectrode electromotive forces Ea and Be corresponds toa value obtained by calculating the difference between the timedifferentials dB1/dt and dB2/dt of the magnetic fields and multiplyingthe difference by a coefficient k (a complex number related to theconductivity and dielectric constant of the fluid to be measured and thestructure of the measuring pipe 1).E=k{−b 2ω0 sin(ω0 t−θ2)+b 1ω0 sin(ω0 t−θ1)}  (7)

Equation (7) can be rewritten to $\begin{matrix}\begin{matrix}{E = {{{- {kb2}}\quad\omega\quad 0\quad{\sin\left( {\omega\quad 0\quad t} \right)}{\cos\left( {- {\theta 2}} \right)}} - {{kb2}\quad\omega\quad 0\quad{\cos\left( {\omega\quad 0\quad t} \right)}{\sin\left( {- {\theta 2}} \right)}} +}} \\{{{kb1}\quad\omega\quad 0\quad{\sin\left( {\omega\quad 0\quad t} \right)}{\cos\left( {- {\theta 1}} \right)}} + {{kb1}\quad\omega\quad 0\quad{\cos\left( {\omega\quad 0\quad t} \right)}{\sin\left( {- {\theta 1}} \right)}}} \\{= {{\left\{ {{{- {b2}}\quad{\sin\left( {{- \theta}\quad 2} \right)}} + {{b1}\quad{\sin\left( {- {\theta 1}} \right)}}} \right\}\omega\quad 0k\quad{\cos\left( {\omega\quad 0t} \right)}} +}} \\{\left\{ {{{- {b2}}\quad{\cos\left( {{- \theta}\quad 2} \right)}} + {{b1}\quad{\cos\left( {- {\theta 1}} \right)}}} \right\}\omega\quad 0k\quad{\sin\left( {\omega\quad 0t} \right)}}\end{matrix} & (8)\end{matrix}$

When equation (8) is mapped onto a complex coordinate plane based onω0t, a real axis component Ex and imaginary axis component Ey are givenbyEx={−b 2 sin(−θ2)+b 1 sin(−θ1)}ω0 k  (9)Ey={−b 2 cos(−θ2)+b 1 cos(−θ1)}ω0 k  (10)

Ex and Ey in equations (9) and (10) are rewritten to $\begin{matrix}\begin{matrix}{{Ex} = {\left\{ {{{- {b2}}\quad{\sin\left( {{- \theta}\quad 2} \right)}} + {{b1}\quad{\sin\left( {- {\theta 1}} \right)}}} \right\}\omega\quad 0k}} \\{= {\left\{ {{{- {b2}}\quad{\cos\left( {{\pi/2} + {\theta\quad 2}} \right)}} + {{b1}\quad{\cos\left( {{\pi/2} + {\theta 1}} \right)}}} \right\}\omega\quad 0k}} \\{= {\left\{ {{{b2}\quad{\cos\left( {{{- \pi}/2} + {\theta\quad 2}} \right)}} + {{b1}\quad{\cos\left( {{\pi/2} + {\theta 1}} \right)}}} \right\}\omega\quad 0k}}\end{matrix} & (11)\end{matrix}$ $\begin{matrix}\begin{matrix}{{Ey} = {\left\{ {{{- {b2}}\quad{\cos\left( {{- \theta}\quad 2} \right)}} + {{b1}\quad{\cos\left( {- {\theta 1}} \right)}}} \right\}\omega\quad 0k}} \\{= {\left\{ {{{- {b2}}\quad{\sin\left( {{\pi/2} + {\theta\quad 2}} \right)}} + {{b1}\quad{\sin\left( {{\pi/2} + {\theta 1}} \right)}}} \right\}\omega\quad 0k}} \\{= {\left\{ {{{b2}\quad{\sin\left( {{{- \pi}/2} + {\theta\quad 2}} \right)}} + {{b1}\quad{\sin\left( {{\pi/2} + {\theta 1}} \right)}}} \right\}\omega\quad 0k}}\end{matrix} & (12)\end{matrix}$to obtain a complex vector Ec given by $\begin{matrix}\begin{matrix}{{Ec} = {{Ex} + {j\quad{Ey}}}} \\{= {{\left\{ {{{b2}\quad{\cos\left( {{{- \pi}/2} + {\theta\quad 2}} \right)}} + {{b1}\quad{\cos\left( {{\pi/2} + {\theta 1}} \right)}}} \right\}\omega\quad 0k} +}} \\{j\left\{ {{{b2}\quad{\sin\left( {{{- \pi}/2} + {\theta\quad 2}} \right)}} + {{b1}\quad{\sin\left( {{\pi/2} + {\theta 1}} \right)}}} \right\}\omega\quad 0k} \\{= {{\left\{ {{{b1}\quad{\cos\left( {{\pi/2} + {\theta\quad 1}} \right)}} + {j\quad{b1}\quad{\sin\left( {{\pi/2} + {\theta\quad 1}} \right)}}} \right\}\omega\quad 0k} +}} \\{\left\{ {{{b2}\quad{\cos\left( {{{- \pi}/2} + {\theta\quad 2}} \right)}} + {j\quad{b2}\quad{\sin\left( {{{- \pi}/2} + {\theta\quad 2}} \right)}}} \right\}\omega\quad 0k} \\{= {{{b1}\quad\omega\quad 0\quad k\quad\exp\left\{ {j\left( {{\pi/2} + {\theta 1}} \right)} \right\}} + {{b2}\quad\omega\quad 0\quad k\quad\exp\left\{ {j\left( {{{- \pi}/2} + {\theta 2}} \right)} \right\}}}}\end{matrix} & (13)\end{matrix}$

The above-described coefficient k can be converted into a complex vectorgiven by$\begin{matrix}\begin{matrix}{k = {{{rk}\quad{\cos\left( {\theta\quad{00}} \right)}} + {j\quad{rk}\quad{\sin\left( {\theta\quad{00}} \right)}}}} \\{= {{rk}\quad{\exp\left( {j\quad\theta\quad{00}} \right)}}}\end{matrix} & (14)\end{matrix}$

In equation (14), rk is a proportional coefficient, and θ00 is the angleof the vector k with respect to the real axis.

When equation (14) is substituted into equation (13), the interelectrodeelectromotive force Ec (an interelectrode electromotive force which iscaused only by a time rate change in magnetic field and is irrelevant tothe flow velocity) converted into the complex vector is given by$\begin{matrix}\begin{matrix}{{Ec} = {{{b1}\quad\omega\quad 0\quad k\quad{\exp\left( {j\left( {{\pi/2} + {\theta 1}} \right)} \right\}}} + {{b2}\quad\omega\quad 0\quad k\quad{\exp\left( {j\left( {{{- \pi}/2} + {\theta 2}} \right)} \right\}}}}} \\{= {{{b1}\quad\omega\quad 0\quad{rk}\quad{\exp\left( {j\left( {{\pi/2} + {\theta 1} + {\theta 00}} \right)} \right\}}} +}} \\{{b2}\quad\omega\quad 0\quad{rk}\quad{\exp\left( {j\left( {{{- \pi}/2} + {{\theta 2}\left( {+ {\theta 00}} \right)}} \right\}} \right.}}\end{matrix} & (15)\end{matrix}$

In equation (15), b1ω0rkexp{j(π/2+θ1+θ00)} is a complex vector whoselength is b1ω0rk and angle from the real axis is π/2+θ1+θ00, andb2ω0rkexp{j(π/2+θ2+θ00)} is a complex vector whose length is b2ω0rk andangle from the real axis is −π/2+θ2+θ00.

The interelectrode electromotive force caused by the flow rate (flowvelocity) of the fluid to be measured will be described next. When theflow velocity of the fluid to be measured is V (V≠0), eddy currents bythe magnetic fields B1 and B2 respectively contain components V×B1 andV×B2 caused by the flow velocity in addition to the eddy currentcomponents Ia and Ib when the flow velocity is 0. For this reason, aneddy current Ia′ by the magnetic field B1 and an eddy current Ib′ by themagnetic field B2 have directions as shown in FIG. 3. Hence, aninterelectrode electromotive force Ea′ generated by the flow velocity Vof the fluid to be measured and the magnetic field B1 and aninterelectrode electromotive force Eb′ generated by the flow velocity Vand the magnetic field B2 have the same direction.

At this time, a total interelectrode electromotive force Ev obtain byadding the interelectrode electromotive forces Ea′ and Eb′ generated bythe flow velocity corresponds to the sum of a value obtained bymultiplying the magnetic field B1 by a coefficient kv (a complex numberrelated to the flow velocity V, the conductivity and dielectric constantof the fluid to be measured, and the structure of the measuring pipe 1)and a value obtained by multiplying the magnetic field B2 by thecoefficient kv.Ev=kv{b 1 cos(ω0 t−θ1)+b 2 cos(ω0 t−θ2)}  (16)

When the term of sin and the term of cos of equation (16) are expanded,we obtain $\begin{matrix}\begin{matrix}{{Ev} = {{{kvb1}\quad{\cos\left( {\omega\quad 0t} \right)}{\cos\left( {- {\theta 1}} \right)}} - {{kvb1}\quad{\sin\left( {\omega\quad 0t} \right)}{\sin\left( {- {\theta 1}} \right)}} +}} \\{{{kvb2}\quad{\cos\left( {\omega\quad 0t} \right)}{\cos\left( {- {\theta 2}} \right)}} - {{kvb2}\quad{\sin\left( {\omega\quad 0t} \right)}{\sin\left( {- {\theta 2}} \right)}}} \\{= {{\left\{ {{{b1}\quad{\cos\left( {- {\theta 1}} \right)}} + {{b2}\quad{\cos\left( {- {\theta 2}} \right)}}} \right\}{kv}\quad{\cos\left( {\omega\quad 0t} \right)}} +}} \\{\left\{ {{{- {b1}}\quad{\sin\left( {- {\theta 1}} \right)}} - {{b2}\quad{\sin\left( {- {\theta 2}} \right)}}} \right\}{kv}\quad{\sin\left( {\omega\quad 0t} \right)}}\end{matrix} & (17)\end{matrix}$

When equation (17) is mapped onto the complex coordinate plane based onω0t, a real axis component Evx and imaginary axis component Evy aregiven byEvx={b 1 cos(−θ1)+b 2 cos(−θ2)}kv  (18)Evy={−b 1 sin(−θ1)−b 2 sin(−θ2)}kv  (19)

Equations (18) and (19) are transformed into a complex vector Evc.$\begin{matrix}\begin{matrix}{{Evx} = {\left\{ {{{b1}\quad{\cos\left( {- {\theta 1}} \right)}} + {{b2}\quad{\cos\left( {- {\theta 2}} \right)}}} \right\}{kv}}} \\{= {\left\{ {{{b1}\quad{\cos\left( {- {\theta 1}} \right)}} + {{b2}\quad{\cos\left( {\theta 2} \right)}}} \right\}{kv}}}\end{matrix} & (20) \\\begin{matrix}{{Evy} = {\left\{ {{{- {b1}}\quad{\sin\left( {- {\theta 1}} \right)}} - {{b2}\quad{\sin\left( {- {\theta 2}} \right)}}} \right\}{kv}}} \\{= {\left\{ {{{b1}\quad{\sin\left( {\theta 1} \right)}} + {{b2}\quad{\sin\left( {\theta 2} \right)}}} \right\}{kv}}}\end{matrix} & (21) \\\begin{matrix}{{Evc} = {{Evx} + {j\quad{Evy}}}} \\{= {{\left\{ {{{b1}\quad{\cos\left( {\theta 1} \right)}} + {{b2}\quad{\cos\left( {\theta 2} \right)}}} \right\}{kv}} + {{j\left( {{{b1}\quad{\sin\left( {\theta 1} \right)}} + {{b2}\quad{\sin\left( {\theta 2} \right)}}} \right\}}{kv}}}} \\{= {{\left\{ {{{b1}\quad{\cos\left( {\theta 1} \right)}} + {j\quad{b1}\quad{\sin\left( {\theta 1} \right)}}} \right\}{kv}} + {\left\{ {{{b2}\quad{\cos\left( {\theta 2}\quad \right)}} + {j\quad{b2}\quad{\sin\left( {\theta 2} \right)}}} \right\}{kv}}}} \\{= {{{b1kv}\quad{\exp\left( {j\quad{\theta 1}} \right)}} + {{b2kv}\quad{\exp\left( {j\quad{\theta 2}} \right)}}}}\end{matrix} & (22)\end{matrix}$

The above-described coefficient kv is transformed to a complex vector$\begin{matrix}\begin{matrix}\left. {{kv} = {{{rkv}\quad{\cos\left( {\theta\quad{01}} \right)}} + {j\quad{rkv}\quad{\sin\left( {\theta 01} \right)}}}} \right\} \\{= {{rkv}\quad{\exp\left( {j\quad{\theta 01}} \right)}}}\end{matrix} & (23)\end{matrix}$

In equation (23), rkv is a proportional coefficient, θ01 is the angle ofthe vector kv with respect to the real axis. In this case, rkvcorresponds to a value obtained by multiplying the proportionalcoefficient rk (equation (14)) by the flow velocity V and a proportionalcoefficient γ. That is,rkv=rkVγ  (24)

When equation (23) is substituted into equation (22), the Interelectrodeelectromotive force Evc converted into complex coordinates is obtainedas $\begin{matrix}\begin{matrix}{{Evc} = {{{b1kv}\quad{\exp\left( {j\quad{\theta 1}} \right)}} + {{b2kv}\quad{\exp\left( {j\quad{\theta 2}} \right)}}}} \\{= {{b1rkv}\quad\exp\left\{ {\left( {j\left( {{\theta 1} + {\theta 01}} \right)} \right\} + {{b2rkv}\quad\exp\left\{ \left( {j\left( {{\theta 2} + {\theta 01}} \right)} \right\} \right.}} \right.}}\end{matrix} & (25)\end{matrix}$

In equation (25), b1rkvexp{j(θ1+θ01)} is a complex vector whose lengthis b1rkv and angle from the real axis is θ1+θ01, and b2rkvexp{j(θ2+θ01)}is a complex vector whose length is b2rkv and angle from the real axisis θ2+θ01.

From equations (15) and (25), a total interelectrode electromotive forceEac obtained by adding the interelectrode electromotive force Ecgenerated by a time-rate change in magnetic field and the interelectrodeelectromotive force Evc generated by the flow velocity of the fluid isgiven by $\begin{matrix}\begin{matrix}{{Eac} = {{Ec} + {Evc}}} \\{= {{{b1}\quad\omega\quad 0{rk}\quad\exp\left\{ {j\left( {{\pi/2} + {\theta 1} + {\theta 00}} \right)} \right\}} +}} \\{{{b2}\quad\omega\quad 0{rk}\quad\exp\left\{ {j\left( {{{- \pi}/2} + {\theta 2} + {\theta 00}} \right)} \right\}} +} \\{{{b1rkv}\quad\exp\left\{ {j\left( {{\theta 1} + {\theta 01}} \right)} \right\}} + {{b2rkv}\quad\exp\left\{ {j\quad\left( {{\theta 2} + {\theta 01}} \right)} \right\}}}\end{matrix} & (26)\end{matrix}$

As is apparent from equation (26), the interelectrode electromotiveforce Eac is described by the four complex vectorsb1ω0rkexp{j(π/2+θ1+θ00)}, b2ω0rkexp{j(−π/2+θ2+θ00)},b1rkvexp{j(θ1+θ01)}, and b2rkvexp{j(θ2+θ01)}. The length of a syntheticvector obtained by synthesizing the four complex vectors represents theamplitude of the output (interelectrode electromotive force Eac), and anangle φ of the synthetic vector represents the phase difference (phasedelay) of the interelectrode electromotive force Eac from the phase ω0tof the input (exciting current).

The present invention will be described below assuming θ1=θ00=θ01=0 foreasy understanding. Accordingly, equation (26) can be rewritten to$\begin{matrix}\begin{matrix}{{Eac} = {{{b1}\quad\omega\quad 0{rk}\quad\exp\left\{ {j\left( {\pi/2} \right)} \right\}} + {{b2}\quad\omega\quad 0{rk}\quad\exp\left\{ {j\left( {{{- \pi}/2} + {\theta 2}} \right)} \right\}} +}} \\{{{b1rkv}\quad\exp\left\{ {j(0)} \right\}} + {{b2rkv}\quad\exp\left\{ {j\left( {\theta 2} \right)} \right\}}} \\{= {{{jb1}\quad\omega\quad 0{rk}} + {{b2}\quad\omega\quad 0{rk}\quad\exp\left\{ {j\left( {{{- \pi}/2} + {\theta 2}} \right)} \right\}} +}} \\{{b1rkv} + {{b2rkv}\quad{\exp\left( {j\quad{\theta 2}} \right)}}}\end{matrix} & (27)\end{matrix}$

At this time, the four vectors representing the interelectrodeelectromotive force Eac has a geometrical relationship shown in FIG. 4.As described above, θ1=0. For this reason, the magnetic field B1generated from the first exciting coil 3 a is B1=b1 cos(ω0t), and themagnetic field B2 generated from the second exciting coil 3 b is B2=b2cos(ω0t−θ2). The phase difference between the magnetic field B1 and themagnetic field B2 is θ2. When the phase difference θ2 between themagnetic fields B1 and B2 is changed, the interelectrode electromotiveforce Eac traces the orbit on the circumference of a circle which has aradius {(b2ω0rk)²+(b2rkv)²}^(1/2) and a center at coordinate points(b1rkv, b1ω0rk) on the complex plane, shown in FIG. 4.

In the above-described basic principle, the conventional electromagneticflowmeter described with reference to FIG. 25 corresponds to a structurein which b1=b2 and θ2=0. This electromagnetic flowmeter detects the flowrate on the basis of the magnitude of the interelectrode electromotiveforce (the length of the synthetic vector).

When b1=b2=0.5β (β is a predetermined physical quantity), and θ2=0 inequation (27), the interelectrode electromotive force Eac is given by$\begin{matrix}\begin{matrix}{{Eac} = {{j\quad{b1}\quad\omega\quad 0{rk}} + {{b2}\quad\omega\quad 0{rk}\quad\exp\left\{ {j\left( {{{- \pi}/2} + {\theta 2}} \right)} \right\}} +}} \\{{b1rkv} + {{b2rkv}\quad{\exp\left( {{j\theta}2} \right)}}} \\{= {{{j0}{.5}\quad\beta\quad\omega\quad 0{rk}} - {{j0}{.5}\quad\beta\quad\omega\quad 0{rk}} + {0.5\quad\beta\quad{rkv}} + {0.5\quad\beta\quad{rkv}}}} \\{= {\beta\quad{rkv}}}\end{matrix} & (28)\end{matrix}$

When the amplitude of the exciting current to the exciting coil 13shifts due to a fluctuation in power supply voltage of the power supplyunit, β corresponding to the amplitude of the magnetic field shifts toβ′ in equation (28). In this case, as shown in FIGS. 5A and 5B, evenwhen the flow rate of the fluid to be measured does not change, thelength of the synthetic vector (the amplitude of the interelectrodeelectromotive force Eac) changes. Hence, a flow rate measurement errordue to the influence of shift of the amplitude of the magnetic fieldoccurs.

First Embodiment

An embodiment of the present invention will be described below indetail. FIG. 6 is a block diagram showing the arrangement of anelectromagnetic flowmeter according to the first embodiment of thepresent invention. The same reference numerals as in FIG. 1 denote thesame components in FIG. 6. The electromagnetic flowmeter according tothis embodiment has a measuring pipe 1, a pair of electrodes 2 a and 2b, an exciting coil 3, a power supply unit 4, a signal conversion unit5, and a flow rate output unit 6A fluid to be measured flows through themeasuring pipe 1. The pair of electrodes 2 a and 2 b oppose each otherin the measuring pipe 1 to be perpendicular to both an axis PAX and themagnetic field applied to the fluid to be measured and also come intocontact with the fluid to be measured. The electrodes 2 a and 2 b detectan electromotive force generated by the magnetic field and the flow ofthe fluid to be measured. A plane PLN which includes the electrodes 2 aand 2 b and is perpendicular to the direction of the measuring pipe axisPAX is defined as a boundary in the measuring pipe 1. In this case, theexciting coil 3 applies asymmetrical magnetic fields to the fluid to bemeasured on both sides of the plane PLN, i.e., the boundary in themeasuring pipe 1. The power supply unit 4 supplies an exciting currentto the exciting coil 3 to generate a magnetic field. The signalconversion unit 5 obtains the phase difference between the excitingcurrent and an interelectrode electromotive force detected by theelectrodes 2 a and 2 b. The flow rate output unit 6 calculates the flowrate of the fluid to be measured on the basis of the phase differenceobtained by the signal conversion unit 5.

In this embodiment, only one exciting coil 3 is used. This correspondsto a structure in which b2=θ2=0 in equation (27) described above. Theexciting coil 3 is arranged at a position separated from the plane PLNby an offset distance d (d>0). Since θ1=0 in equation (3) of themagnetic field generated from the exciting coil 3 when the excitingcurrent is supplied from the power supply unit 4, a magnetic fieldcomponent B1 which is perpendicular, on an electrode axis EAX thatconnects the electrodes 2 a and 2 b, to both the electrode axis EAX andthe measuring pipe axis PAX is given byB1=b1 cos(ω0t)  (29)

When b2=θ2=0 in equation (27), we obtainEac=jb 1ω0 rk+b 1 rkv  (30)

FIGS. 7A and 7B show the principle of flow rate measurement in which theamplitude shift of the magnetic field is corrected in this embodiment.Two vectors representing an interelectrode electromotive force Eac givenby equation (30) have a geometrical relationship shown in FIG. 7A. FromFIG. 7A and equation (30), we obtain $\begin{matrix}\begin{matrix}{{\tan\left( {{\pi/2} - \phi} \right)} = {({b1rkv})/\left( {{b1}\quad\omega\quad 0{rk}} \right)}} \\{= {{rkv}/\left( {\omega\quad 0{rk}} \right)}}\end{matrix} & (31)\end{matrix}$

Assume that an amplitude b1 of the magnetic field B1 shifts to b1′. Thegeometrical relationship between the two vectors representing theinterelectrode electromotive force Eac changes from FIG. 7A to FIG. 7B.Equation (31) is rewritten to $\begin{matrix}\begin{matrix}{{\tan\left( {{\pi/2} - \phi^{\prime}} \right)} = {\left( {{b1}^{\prime}{rkv}} \right)/\left( {{b1}^{\prime}\quad\omega\quad 0{rk}} \right)}} \\{= {{rkv}/\left( {\omega\quad 0{rk}} \right)}}\end{matrix} & (32)\end{matrix}$

Since the right-hand side of equation (31) equals that of equation (32),φ=φ′ holds. More specifically, when the amplitude b1 of the magneticfield B1 shifts to b1′, the amplitude of the interelectrodeelectromotive force Eac (the length of the synthetic vector) changes toFIG. 7B. However, a phase difference φ between a phase ω0t of theexciting current (magnetic field B1) and the interelectrodeelectromotive force Eac is kept unchanged unless the flow rate of thefluid to be measured changes. Hence, when the flow rate is detected onthe basis of the phase difference φ, the flow rate measurement error dueto the influence of the shift can automatically be canceled.

To obtain the flow rate of the fluid to be measured, equation (31) isrewritten torkv=ω0 rk tan(π/2−φ)  (33)

On the basis of equation (24), equation (33) can be rewritten toV=α1×tan(π/2−φ) for α1=ω0/γ  (34)where α1 (or γ) is a coefficient predetermined by calibration or thelike. The signal conversion unit 5 detects the electromotive force Eacbetween the electrodes 2 a and 2 b and obtains the phase difference φbetween the phase ω0t of the exciting current and the interelectrodeelectromotive force Eac. The flow rate output unit 6 calculates a flowvelocity V of the fluid to be measured, i.e., the flow rate per unittime by using equation (34) on the basis of the phase difference φobtained by the signal conversion unit 5.

As described above, as the basic technical idea of the presentinvention, asymmetrical magnetic fields are applied to the fluid to bemeasured on both sides of the plane PLN in the measuring pipe 1 togenerate a phase difference between the input (exciting current) and theoutput (electromotive force). A flow rate measurement error due to theshift of the magnetic field state is corrected or removed on the basisof the mechanism of the phase difference. In this embodiment, the flowrate is calculated by using an asymmetrical exciting characteristicparameter. (the phase difference φ between the exciting current and theinterelectrode electromotive force Eac) which depends on the flow rateof the fluid to be measured and does not depend on the shift of theamplitude of the magnetic field B1. Accordingly, the flow rate can becalculated while automatically canceling the flow rate measurement errordue to the influence of in-phase component noise (the shift of theamplitude of the magnetic field). Hence, accurate flow rate measurementcan be executed.

Second Embodiment

FIG. 8 is a block diagram showing the arrangement of an electromagneticflowmeter according to the second embodiment of the present invention.The same reference numerals as in FIGS. 1 and 6 denote the samecomponents in FIG. 8. The electromagnetic flowmeter according to thisembodiment has a measuring pipe 1, electrodes 2 a and 2 b, first andsecond exciting coils 3 a and 3 b, a power supply unit 4 a, a signalconversion unit 5, and a flow rate output unit 6 a. A plane PLN whichincludes the electrodes 2 a and 2 b and is perpendicular to thedirection of a measuring pipe axis PAX is defined as a boundary in themeasuring pipe 1. In this case, the first and second exciting coils 3 aand 3 b apply asymmetrical magnetic fields to the fluid to be measuredon both sides of the plane PLN, i.e., the boundary in the measuring pipe1. The power supply unit 4 a supplies exciting currents having the samefrequency and same phase to the first and second exciting coils 3 a and3 b to generate magnetic fields. The signal conversion unit 5 obtainsthe phase difference between the exciting current and an interelectrodeelectromotive force detected by the electrodes 2 a and 2 b. The flowrate output unit 6 a calculates the flow rate of the fluid to bemeasured on the basis of the phase difference obtained by the signalconversion unit 5.

This embodiment corresponds to a structure in which b1≠b2, and θ2=0 inequation (27) described above. The first exciting coil 3 a is arranged,e.g., downstream of the plane PLN at a position separated from, it by anoffset distance d1. The second exciting coil 3 b is arranged, e.g.,upstream of the plane PLN at a position separated from it by an offsetdistance d2, i.e., on the opposite side of the first exciting coil 3 awith respect to the plane PLN. Exciting currents having the samefrequency, same phase, and different amplitudes are supplied from thepower supply unit 4 a. Accordingly, asymmetrical magnetic fields areformed on both sides of the plane PLN in the measuring pipe 1.

Of the magnetic field generated from the first exciting coil 3 a whenthe exciting current is supplied from the power supply unit 4 a, amagnetic field component B1 which is perpendicular, on an electrode axisEAX that connects the electrodes 2 a and 2 b, to both the electrode axisEAX and the measuring pipe axis PAX is given by equation (35) becauseθ1=0 in equation (3). Of the magnetic field generated from the secondexciting coil 3 b, a magnetic field component B2 which is perpendicularto both the electrode axis EAX and the measuring pipe axis PAX on theelectrode axis EAX is given by equation (36) because θ2=0 in equation(4)B1=b1 cos(ω0t)  (35)B2=b2 cos(ω0t)  (36)

When θ2=0 in equation (27), we obtain

 Eac=jb 1ω0 rk−jb 2ω0 rk+b 1 rkv+b 2 rkv  (37)

FIGS. 9A and 9B show the principle of flow rate measurement of in thisembodiment. Four vectors representing an interelectrode electromotiveforce Eac given by equation (37) have a geometrical relationship shownin FIG. 9A. From FIG. 9A and equation (37), we obtaintan(π/2−φ)={(b 1+b 2)rkv}/{(b 1−b 2)ω0 rk}  (38)

Assume that an amplitude b1 of the magnetic field B1 shifts to b1′, andan amplitude b2 of the magnetic field B2 shifts to b2′. The geometricalrelationship between the four vectors representing the interelectrodeelectromotive force Eac changes from FIG. 9A to FIG. 9B. Equation (38)is rewritten totan(π/2−φ′)={(b 1′+b 2′)rkv}/{(b 1′−b 2′)ω0 rk}  (39)

The power supply unit 4 a which supplies the exciting currents iscommonly used for the first exciting coil 3 a and second exciting coil 3b. Hence, even when the amplitude b1 shifts to b1′, and the amplitude b2shifts to b2′, the following relationship holdsb 1′/b 1=b 2′/b 2=ρ  (40)

From equation (40), equation (39) is written to $\begin{matrix}\begin{matrix}{{\tan\left( {{\pi/2} - \phi^{\prime}} \right)} = {\left\{ {{\rho\left( {{b1} + {b2}} \right)}{rkv}} \right\}/\left\{ {{\rho\left( {{b1} - {b2}} \right)}\omega\quad 0{rk}} \right\}}} \\{= {\left\{ {\left( {{b1} + {b2}} \right){rkv}} \right\}/\left\{ {\left( {{b1} - {b2}} \right)\omega\quad 0{rk}} \right\}}}\end{matrix} & (41)\end{matrix}$

Since the right-hand side of equation (38) equals that of equation (41),φ=φ′ holds. More specifically, when the amplitude b1 of the magneticfield B1 shifts to b1′, and the amplitude b2 of the magnetic field B2shifts to b2′, the amplitude of the interelectrode electromotive forceEac (the length of the synthetic vector) changes to FIG. 9B. However, aphase difference φ between a phase ω0t of the exciting current (magneticfields B1 and B2) and the interelectrode electromotive force Eac is keptunchanged unless the flow rate of the fluid to be measured changes.Hence, when the flow rate is detected on the basis of the phasedifference φ, the flow rate measurement error due to the influence ofthe shift can automatically be canceled.

To obtain the flow rate of the fluid to be measured, equation (38) isrewritten torkv={(b 1−b 2)/(b 1+b 2)}ω0 rk tan(π/2−φ)  (42)

On the basis of equation (24), equation (42) can be rewritten toV=α1×tan(π/2−φ) for α1={(b 1−b 2)/(b 1+b 2)}ω0/γ  (43)where α1 (or γ) is a coefficient predetermined by calibration. As in thefirst embodiment, the signal conversion unit 5 detects the electromotiveforce Eac between the electrodes 2 a and 2 b and obtains the phasedifference φ between the phase ω0t of the exciting currents (magneticfields B1 and B2) and the interelectrode electromotive force Eac. Theflow rate output unit 6 a calculates a flow velocity V of the fluid tobe measured by using equation (43) on the basis of the phase differenceφ obtained by the signal conversion unit 5. With the above arrangement,the same effect as in the first embodiment can be obtained.

Third Embodiment

FIG. 10 is a block diagram showing the arrangement of an electromagneticflowmeter according to the third embodiment of the present invention.The same reference numerals as in FIGS. 1, 6, and 8 denote the samecomponents in FIG. 10. In the second embodiment, the offset distance d1from the plane PLN to the axis of the first exciting coil 3 a equals theoffset distance d2 from the plane PLN to the axis of the second excitingcoil 3 b so that the exciting coils are arranged symmetrically. Instead,as shown in FIG. 10, first and second exciting coils 3 a and 3 b may bearranged at different offset distances d1 and d2.

In this embodiment, since asymmetrical magnetic fields can be formed onboth sides of a plane PLN in a measuring pipe 1 by asymmetricallyarranging the first and second exciting coils 3 a and 3 b. For thisreason, the same exciting current may be supplied for a power supplyunit 4 a to the first and second exciting coils 3 a and 3 b. Theremaining components are the same as in the second embodiment.

Fourth Embodiment

FIG. 11 is a block diagram showing the arrangement of an electromagneticflowmeter according to the fourth embodiment of the present invention.The same reference numerals as in FIGS. 1, 6, and 8 denote the samecomponents in FIG. 11. In the second embodiment, the angle made by theelectrode axis EAX and the axis of the first exciting coil 3 a equalsthat made by the electrode axis EAX and the axis of the second excitingcoil 3 b (both angles are 90°). Instead, as shown in FIG. 11, first andsecond exciting coils 3 a and 3 b may be arranged such that the anglemade by an electrode axis EAX and the axis of the first exciting coil 3a becomes different from that made by the electrode axis EAX and theaxis of the second exciting coil 3 b.

Accordingly, magnetic fields B1 and B2 can have different amplitudes b1and b2. For this reason, the same exciting current may be supplied for apower supply unit 4 a to the first and second exciting coils 3 a and 3b. The remaining components are the same as in the second embodiment.

Fifth Embodiment

FIG. 12 is a block diagram showing the arrangement of an electromagneticflowmeter according to the fifth embodiment of the present invention.The same reference numerals as in FIGS. 1, 6, and 8 denote the samecomponents in FIG. 12. The electromagnetic flowmeter according to thisembodiment has a measuring pipe 1, electrodes 2 a and 2 b, first andsecond exciting coils 3 a and 3 b, a power supply unit 4 b, a signalconversion unit 5 b, and a flow rate output unit 6 b. Exciting currentssupplied to the first and second exciting coils 3 a and 3 b have thesame frequency. The power supply unit 4 b supplies the exciting currentsto the first and second exciting coils 3 a and 3 b while changing thephase difference between the exciting currents to generate magneticfields. The signal conversion unit 5 b obtains the amplitude of aninterelectrode electromotive force detected by the electrodes 2 a, and 2b in each of at least two states in which the exciting currents havedifferent phase differences, and obtains the ratio of the amplitudes.The flow rate output unit 6 b calculates the flow rate of the fluid tobe measured on the basis of the amplitude ratio obtained by the signalconversion unit 5 b.

This embodiment corresponds to a structure in which b1=b2 in equation(27) described above. For the descriptive convenience, amplitudes b1 andb2 of magnetic fields B1 and B2 have a relationship given by b1=b2=b.The first and second exciting coils 3 a and 3 b can have any arrangementas long as b1=b2 can hold. The exciting coils can be arranged eithersymmetrically as in the second embodiment, or asymmetrically as in thethird or fourth embodiment. Exciting currents to be supplied to thefirst and second exciting coils 3 a and 3 b can have either the sameamplitude or different amplitudes.

Since b1=b, and θ1=0 in equation (3), the magnetic field B1 generatedfrom the first exciting coil 3 a is given by equation (44). Since b2=bin equation (4), the magnetic field B2 generated from the secondexciting coil 3 b is given by equation (45).B1=b cos(ω0t)  (44)B 2=b cos(ω0 t−θ2)  (45)

When b1=b2=b in equation (27), we obtainsEac=jbω0 rk+bω0 rkexp{j(−π/2+θ2)}+brkv+brkvexp(jθ2)  (46)

FIGS. 13 to 18 show the principle of flow rate measurement in thisembodiment. Four vectors representing an interelectrode electromotiveforce Eac given by equation (46) have a geometrical relationship shownin FIG. 13. Referring to FIG. 13, vectors corresponding to therespective terms of equation (46) when the flow rate is not 0 areindicated by solid lines. The locus of the synthetic vector forms acircle having a center at (brkv,bω0rk) on the complex plane. When theflow rate is 0, the third and fourth terms of equation (46) are 0.Hence, the locus of the synthetic vector forms a circle having a centerat (0,bω0rk) on the complex plane.

As shown in FIGS. 14 to 16, an angle φ (the phase difference between aphase ω0t and the interelectrode electromotive force Eac) of thesynthetic vector obtained by synthesizing the four vectors of equation(46) is ½ a phase difference θ2 between the exciting current supplied tothe first exciting coil 3 a and that supplied to the second excitingcoil 3 b (the magnetic fields B1 and B2). This relationship will bedescribed below.

FIG. 14 shows the geometrical relationship between the four vectors ofequation (46) when θ2<π (180°). When the flow rate of the fluid to bemeasured is 0, equation (46) can be rewritten toEac=jbω0 rk+bω0 rkexp{j(−π/2+θ2)}  (47)

When the flow rate is 0, ΔABC formed by two complex vectors jbω0rk andbω0rkexp{j(−π/2+θ2)} and their synthetic vector is an isoscelestriangle. The magnitude of an angle <ABC made by sides AB and BC is(π−θ2)/2. At this time, the angle (phase) of the synthetic vector isd1=θ2/2.

On the other hand, ΔCDE formed by two vectors brkv and brkvexp(jθ2)generated when the flow rate is not 0 is an isosceles triangle. Themagnitude of an angle <ECD made by sides EC and CD is θ2/2. That is,when the flow rate of the fluid to be measured increases, the angle ofthe synthetic vector is θ2=θ2/2.

FIG. 15 shows the geometrical relationship between the four vectors ofequation (46) when θ2>π (180°). When the flow rate of the fluid to bemeasured is 0, ΔABC formed by the two complex vectors jbω0rk andbω0rkexp{j(−π/2+θ2)} and their synthetic vector is an isoscelestriangle. The magnitude of the angle <ABC is (θ2−π)/2. At this time, anangle φ1′+π/2 of the synthetic vector is θ2/2.

On the other hand, ΔCDE formed by the two vectors brkv and brkvexp(jθ2)generated when the flow rate is not 0 is an isosceles triangle. Themagnitude of the angle <ECD is {π−(θ2−π)}/2=−θ2/2. That is, when theflow rate of the fluid to be measured increases, the direction (phase)in which the synthetic vector changes is φ2′+π/2=(π/2−/<ECD)+π/2=θ2/2from C to D in FIG. 15.

FIG. 16 shows the geometrical relationship between the four vectors ofequation (46) when θ2+=π (180°). When the flow rate of the fluid to bemeasured is 0, the synthetic vector is on an imaginary axis Y of thecomplex vectors. The two vectors brkv and brkvexp(jθ2) generated whenthe flow rate is not 0 have the same magnitude and reverse directions.Hence, the end point of the synthetic vector does not change. Morespecifically, when θ2=π, the angle of the synthetic vector is alwaysθ2/2=π/2. The interelectrode electromotive force Eac remains constantindependlety of the flow rate.

As described above, the phase φ of the synthetic vector is ½ the phasedifference θ2 between the exciting current supplied to the firstexciting coil 3 a and that supplied to the second exciting coil 3 b andis not affected by the flow rate of the fluid to be measured. That is,when the flow rate changes, the end point of the synthetic vector movesas shown in FIG. 17 while maintaining the phase difference θ2. Thecharacteristic of the prior art corresponds to movement on the realaxis.

When θ2=0 in equation (46), we obtainEac=brkv+brkv  (48)

When θ2=π in equation (46), we obtainEac=jbω0 rk+jbω0 rk  (49)

FIGS. 18A and 18B show the principle of flow rate measurement with shiftcorrection in this embodiment. FIG. 18A shows the geometricalrelationship between two vectors representing the interelectrodeelectromotive force Eac when θ2=0 and the geometrical relationshipbetween two vectors representing the interelectrode electromotive forceEac when θ2=π.

From FIG. 18A and equations (48) and (49), a ratio R of an amplitude(the length of the synthetic vector) A_(θ2=0) of the interelectrodeelectromotive force Eac when the phase difference θ2=0 to the amplitudeA_(θ2=0) of the interelectrode electromotive force Eac when the phasedifference θ2=π is given by $\begin{matrix}\begin{matrix}{R = {{A_{{\theta 2} = 0}/A_{{\theta 2} = \pi}} = {\left( {{brkv} + {brkv}} \right)/\left( {{b\quad{\omega 0rk}} + {b\quad\omega\quad 0{rk}}} \right)}}} \\{= {{rkv}/\left( {\omega\quad 0{rk}} \right)}}\end{matrix} & (50)\end{matrix}$

Assume that an amplitude b of the magnetic fields B1 and B2 shifts tob′. The geometrical relationship between the vectors representing theinterelectrode electromotive force Eac changes from FIG. 18A to FIG.18B. Equation (50) is rewritten to $\begin{matrix}\begin{matrix}{R^{\prime} = {A_{{\theta 2} = 0}^{\prime}/A_{{\theta 2} = \pi}^{\prime}}} \\{= {\left( {{b^{\prime}{rkv}} + {b^{\prime}{rkv}}} \right)/\left( {{b^{\prime}\omega\quad 0{rk}} + {b^{\prime}\omega\quad 0{rk}}} \right)}} \\{= {{rkv}/\left( {\omega\quad 0{rk}} \right)}}\end{matrix} & (51)\end{matrix}$

Since the right-hand side of equation (50) equals that of equation (51),R=R′ holds. More specifically, the amplitude ratio R of theinterelectrode electromotive force Eac does not change even when theamplitude b of the magnetic fields B1 and. B2 shifts to b′. Whileswitching is executed by the power supply unit 4 b such that the phasedifference θ2 between the exciting current supplied to the firstexciting coil 3 a and that supplied to the second exciting coil 3 btakes two values, an amplitude is obtained in correspondence with eachvalue. When the flow rate is detected on the basis of the amplituderatio R, the flow rate measurement error due to the influence of theshift can automatically be canceled.

To obtain the flow rate of the fluid to be measured, equation (50) isrewritten torkv=ω0 rk(A _(θ2=0) /A _(θ2=π))=ω0 rkR  (52)

On the basis of equation (24), equation (52) can be rewritten toV=α2×R for α2=ω0/γ  (53)

Equation (53) is the formula of the flow velocity V when excitingcurrents with the phase difference θ2=0 and exciting currents with thephase difference θ2=π are supplied to the first and second excitingcoils 3 a and 3 b. A formula generalized from equation (53) will bederived next. Referring to FIG. 14, a magnitude |BE| of the syntheticvector obtained by synthesizing the four vectors of equation (46) isgiven by|BE|=2La+2Lb for La=bω0 rk sin(θ2/2) Lb=brkv cos(θ2/2)  (54)where La is a length obtained by dividing a line segment BC in FIG. 14into two equal parts, and Lb is a length obtained by dividing a linesegment CE in FIG. 14 into two equal parts. From equation (54), weobtain|BE|=2bω0 rk sin(θ2/2)+2brkv cos(θ2/2)  (55)

Next, an arbitrary value χ(χ is a real number) which satisfies phasedifference θ2=2χ is taken. At this time, from equation (55), a magnitude|BE|_(θ2=2χ) of the synthetic vector BE is given by|BE| _(θ2=2χ)=2bω0 rk sin χ+2brkv cos χ  (56)

An arbitrary value ψ (ψ is a real number) which satisfies phasedifference θ2=2ψ is taken. At this time, from equation (55) a magnitude|BE|_(θ2=2ψ) of the synthetic vector BE is given by|BE| _(θ2=2ψ)=2bω0 rk sin ψ+2brkv cos ψ  (57)

|BE|_(θ2=2χ) is an amplitude A_(θ2=2χ) of the interelectrodeelectromotive force Eac when phase difference θ2=2χ. |BE|_(θ2=2ψ) is anamplitude A_(θ2=2ψ) of the interelectrode electromotive force Eac whenphase difference θ2=2ψ. From equations (56) and (57) the ratio R of theamplitude A_(θ2=2χ) of the interelectrode electromotive force Eac whenphase difference θ2=2χ to the amplitude A_(θ2=2ψ) of the interelectrodeelectromotive force Eac when phase difference θ2=2ψ is given by$\begin{matrix}\begin{matrix}{R = {A_{{\theta 2} = {2\chi}}A_{{\theta 2} = {2\phi}}}} \\{= {\left( {{2b\quad\omega\quad 0{rk}\quad\sin\quad\chi} + {2{brkv}\quad\cos\quad\chi}} \right)/\left( {{2b\quad\omega\quad 0{rk}\quad\sin\quad\psi} + {2{brkv}\quad\cos\quad\psi}} \right)}} \\{= {\left( \quad{{\omega\quad 0{rk}\quad\sin\quad\chi} + {{rkv}\quad\cos\quad\chi}} \right)/\left( \quad{{\omega\quad 0{rk}\quad\sin\quad\psi} + {{rkv}\quad\cos\quad\psi}} \right)}}\end{matrix} & (58)\end{matrix}$

Equation (58) representing the ratio R of the amplitude of theinterelectrode electromotive force Eac has no term of the amplitude b ofthe magnetic fields B1 and B2. For this reason, even when the amplitudeb of the magnetic fields B1 and B2 shifts, the ratio R does not change.Hence, while switching is executed by the power supply unit 4 b suchthat the phase difference θ2 between the exciting current supplied tothe first exciting coil 3 a and that supplied to the second excitingcoil 3 b takes the two values 2χ and 2ψ, an amplitude is obtained incorrespondence with each value. When the flow rate is detected on thebasis of the amplitude ratio R, the flow rate measurement error due tothe influence of the shift can automatically be canceled.

When P=ω0rk and Q=rkv, equation (58) can be rewritten to $\begin{matrix}{\begin{matrix}{\left. {R = {{P\quad\sin\quad\chi} + {Q\quad\cos\quad\chi}}} \right)/\left( {{P\quad\sin\quad\psi} + {Q\quad\cos\quad\psi}} \right)} \\{= \left\{ {\left( {P^{2} + Q^{2}} \right)^{1/2}{{\sin\left( {\chi + \tau} \right)}/\left( {P^{2} + Q^{2}} \right)^{1/2}}{\sin\left( {\psi + \tau} \right)}} \right\}}\end{matrix}{{{for}\quad\tau} = {\tan^{- 1}\left( {Q/P} \right)}}} & (59)\end{matrix}$

From equation (59), we obtain $\begin{matrix}\begin{matrix}{R = {{\sin\left( {\chi + \tau} \right)}/{\sin\left( {\psi + \tau} \right)}}} \\{= {\left( {{\sin\quad\chi\quad\cos\quad\tau} + {\cos\quad\chi\quad\sin\quad\tau}} \right)/\left( {{\sin\quad\psi\quad\cos\quad\tau} + {\cos\quad\psi\quad\sin\quad\tau}} \right)}} \\{= {\left( {{\sin\quad\chi} + {\cos\quad\chi\quad\tan\quad\tau}} \right)/\left( {{\sin\quad\psi} + {\cos\quad\psi\quad\tan\quad\tau}} \right)}}\end{matrix} & (60)\end{matrix}$

From equation (60), we obtain

 R sin ψ+R cos ψtan τ=sin χ+cos χtan τ  (61)

From equation (61), we obtaintan τ (R cost ψ−cos χ)=sin χ−R sinψ  (62)

From equation (62), we obtaintan τ=(−R sin ψ+sin χ)/(R cosψ−cos χ)  (63)

From τ=tan⁻¹(Q/P), we obtaintan τ=Q/P=rkv/(ω0 rk)  (64)

From equations (64) and (24), equation (63) can be rewritten to$\begin{matrix}{\begin{matrix}{V = {\left( {\omega\quad{0/\gamma}} \right) \times \left\{ {\left( {{{- R}\quad\sin\quad\psi} + {\sin\quad\chi}} \right)/\left( {{R\quad\cos\quad\psi} - {\cos\quad\chi}} \right)} \right\}}} \\{= {\left( {{- \omega}\quad{0/\gamma}} \right) \times \left\{ {\left( {{R\quad\sin\quad\psi} - {\sin\quad\chi}} \right)/\left( {{R\quad\cos\quad\psi} - {\cos\quad\chi}} \right)} \right\}}} \\{= {\alpha\quad 2 \times \left\{ {\left( {{R\quad\sin\quad\psi} - {\sin\quad\chi}} \right)/\left( {{R\quad\cos\quad\psi} - {\cos\quad\chi}} \right)} \right\}}}\end{matrix}{{{for}\quad\alpha\quad 2} = {{- \omega}\quad{0/\gamma}}}} & (65)\end{matrix}$where α2 (or γ) is a coefficient predetermined by calibration or thelike. With the above processing, the formula of the flow velocity V whenexciting currents with the phase difference θ2=2χ and exciting currentswith the phase difference θ2=2ψ are supplied to the first and secondexciting coils 3 a and 3 b can be obtained. Equation (65) is obtained bygeneralizing equation (53). When θ2=2χ=0 and θ2=2ψ=π in equation (65),equation (53) can be obtained.

The power supply unit 4 b supplies exciting currents with the phasedifference θ2=2χ and exciting currents with the phase difference θ2=2ψto the first and second exciting coils 3 a and 3 b. The signalconversion unit 5 b obtains the amplitude of the interelectrodeelectromotive force Eac detected by the electrodes 2 a and 2 b in eachof the two states with different phase differences θ2 and obtains theratio R of the amplitudes. The flow rate output unit 6 b calculates theflow velocity V of the fluid to be measured by using equation (65) onthe basis of the amplitude ratio R obtained by the signal conversionunit 5 b. With the above arrangement, the same effect as in the firstembodiment can be obtained. As a characteristic feature of thisembodiment, a plurality of predetermined discrete values are used forthe phase difference θ2. The phase difference θ2 is not limited to twovalues.

Sixth Embodiment

The sixth embodiment of the present invention will be described next. Anelectromagnetic flowmeter according to this embodiment has the samearrangement as that of the fifth embodiment, and a description thereofwill be made with reference to FIG. 12. A power supply unit 4 b of thisembodiment supplies exciting currents having the same frequency to firstand second exciting coils 3 a and 3 b and continuously switches thephase difference between the exciting currents. A signal conversion unit5 b obtains the amplitude of an interelectrode electromotive forcedetected by electrodes 2 a and 2 b in each of a plurality of states withdifferent phase differences between the exciting currents and obtains aphase difference between the exciting currents corresponding to theamplitude having a predetermined value. On the basis of the phasedifference obtained by the signal conversion unit 5 b, a flow rateoutput unit 6 b calculates the flow rate of a fluid to be measured.

This embodiment corresponds to a structure in which b1=b2 in equation(27) described above. For the descriptive convenience, b1=b2=b. Thefirst and second exciting coils 3 a and 3 b can have any arrangement aslong as b1=b2 can hold. The exciting coils can be arranged eithersymmetrically as in the second embodiment, or asymmetrically as in thethird or fourth embodiment. Exciting currents to be supplied from thepower supply unit 4 b to the first and second exciting coils 3 a and 3 bcan have either the same amplitude or different amplitudes.

A magnetic field B1 generated from the first exciting coil 3 a when theexciting current is supplied from the power supply unit 4 b is given byequation (44). A magnetic field B2 generated from the second excitingcoil 3 b is given by equation (45).

When b1=b2=b in equation (27), an interelectrode electromotive force Eacis given by equation (46). Four vectors representing the interelectrodeelectromotive force Eac have a geometrical relationship shown in FIG. 13described in the fifth embodiment. The principle of the fifth embodimentdescribed with reference to FIGS. 14 to 17 also holds in thisembodiment.

FIGS. 19 and 20 show the principle of flow rate measurement in thisembodiment. When a phase difference θ2 between the exciting currentsupplied to the first exciting coil 3 a and the exciting currentsupplied to the second exciting coil 3 b is continuously changed, thephase difference θ2, for which the length of the synthetic vector of thefour vector of equation (46) becomes 0 (the start point and end point ofthe synthetic vector are the same), is always present. FIG. 19 shows astate in which the length of the synthetic vector is 0.

At this time, a phase difference θ2 _(A=0) is given byθ2 _(A=0)=2π−2 tan³¹ ¹ {rkv/ω0 rk}  (66)

That is, the phase difference θ2 ₌₀ changes in accordance with the flowrate (rkv) of the fluid to be measured. However, the phase difference θ2_(A=0) does not depend on an amplitude b of the magnetic fields B1 andB2. As shown in FIGS. 20A and 20B, even when the amplitude b of themagnetic fields B1 and B2 shifts to b′, phase difference θ2 _(A=0) doesnot change while continuously changing the phase difference θ2, thelength of the synthetic vector (the amplitude of the interelectrodeelectromotive force Eac) is obtained. When the flow rate is detected onthe basis of the phase difference θ2 _(A=0) for which the length becomes0, the flow rate measurement error due to the influence of the shift canautomatically be canceled.

To obtain the flow rate of the fluid to be measured, equation (66) isrewritten to $\begin{matrix}\begin{matrix}{{rkv} = {\omega\quad 0\quad{rk}\quad\tan\left\{ {\left( {{2\quad\pi} - {\theta\quad 2_{A = 0}}} \right)/2} \right\}}} \\{= {{- \omega}\quad 0\quad{rk}\quad{\tan\left( {\theta\quad{2_{A = 0}/2}} \right)}}}\end{matrix} & (67)\end{matrix}$

On the basis of equation (24), equation (67) can be rewritten toV=α3×tan(θ2 _(A=0)/2) for α3=−ω0/γ  (68)where α3 is a coefficient predetermined by calibration or the like. Thepower supply unit 4 b continuously switches the phase difference θ2between the exciting current supplied to the first exciting coil 3 a andthe exciting current supplied to the second exciting coil 3 b. Thesignal conversion unit 5 b obtains the amplitude of the interelectrodeelectromotive force Eac detected by the electrodes 2 a and 2 b in eachof the plurality of states with different phase differences θ2 andobtains the phase difference θ2 _(A=0) for which the amplitude Eac has apredetermined value of 0. The flow rate output unit 6 b calculates aflow velocity V of the fluid to be measured by using equation (68) onthe basis of the phase difference θ2 _(A=0) obtained by the signalconversion unit 5 b. With the above arrangement, the same effect as inthe first embodiment can be obtained.

Seventh Embodiment

The seventh embodiment of the present invention will be described next.An electromagnetic flowmeter according to this embodiment has the samearrangement as that of the fifth embodiment, and a description thereofwill be made with reference to FIG. 12. A power supply unit 4 b of thisembodiment supplies exciting currents having the same frequency ω0 and apredetermined phase difference θ2 to first and second exciting coils 3 aand 3 b. The power supply unit 4 b supplies the exciting currents to thefirst and second exciting coils 3 a and 3 b while changing the frequencyω0. A signal conversion unit 5 b obtains the amplitude of aninterelectrode electromotive force detected by electrodes 2 a and 2 b ineach of at least two states with different frequencies ω0 of theexciting currents and obtains the ratio of the amplitudes. On the basisof the amplitude ratio obtained by the signal conversion unit 5 b, aflow rate output unit 6 b calculates the flow rate of a fluid to bemeasured.

This embodiment corresponds to a structure in which b1=b2 in equation(27) described above. For the descriptive convenience, b1=b2=b. Thefirst and second exciting coils 3 a and 3 b can have any arrangement aslong as b1=b2 can hold. The exciting coils can be arranged eithersymmetrically as in the second embodiment or asymmetrically as in thethird or fourth embodiment. Exciting currents to be supplied from thepower supply unit 4 b to the first and second exciting coils 3 a and 3 bcan have either the same amplitude or different amplitudes.

A magnetic field B1 generated from the first exciting coil 3 a when theexciting current is supplied from the power supply unit 4 b is given byequation (44). A magnetic field B2 generated from the second excitingcoil 3 b is given by equation (45).

When b1=b2=b in equation (27), an interelectrode electromotive force Eacis given by equation (46). Four vectors representing the interelectrodeelectromotive force Eac have a geometrical relationship shown in FIG. 13described in the fifth embodiment. The principle of the fifth embodimentdescribed with reference to FIGS. 14 to 17 also holds in thisembodiment.

FIGS. 21A and 21B show the principle of flow rate measurement in thisembodiment. When the frequency ω0 of the exciting current is ω1, fourvectors representing the interelectrode electromotive force Eac have ageometrical relationship shown in FIG. 21A. When the frequency ω0 is ω2,the four vectors representing the interelectrode electromotive force Eachave a geometrical relationship shown in FIG. 21B.

Referring to FIG. 14, a magnitude |BE| of a synthetic vector BE obtainedby synthesizing the four vectors of equation (46) is given by equation(54). From equation (54), a ratio Ror of an amplitude A _(ω0=ω1) of theinterelectrode electromotive force Eac when the frequency ω0=ω1 to anamplitude A_(ω0=ω2) of the interelectrode electromotive force Eac whenthe frequency ω0=ω2 is given by $\begin{matrix}\begin{matrix}{{Ror} = {A_{{\omega\quad 0} = {\omega\quad 1}}/A_{{\omega\quad 0} = {\omega\quad 2}}}} \\{= {\left\{ {{2b\quad\omega\quad 1\quad{rk}\quad{\sin\left( {\theta\quad{2/2}} \right)}} + {2{brkv}\quad{\cos\left( {\theta\quad{2/2}} \right)}}} \right\}/}} \\{\left\{ {{2b\quad\omega\quad 2{rk}\quad{\sin\left( {\theta\quad{2/2}} \right)}} + {2{brkv}\quad{\cos\left( {\theta\quad{2/2}} \right)}}} \right\}} \\{= {\left\{ {{\omega\quad 1\quad{rk}\quad{\sin\left( {\theta\quad{2/2}} \right)}} + {{rkv}\quad{\cos\left( {\theta\quad{2/2}} \right)}}} \right\}/}} \\{\left\{ {{\omega\quad 2\quad{rk}\quad{\sin\left( {\theta\quad{2/2}} \right)}} + {{rkv}\quad{\cos\left( {\theta\quad{2/2}} \right)}}} \right\}}\end{matrix} & (69)\end{matrix}$

Equation (69) representing the ratio Ror has no term of an amplitude bof the magnetic fields B1 and B2. For this reason, even when theamplitude b of the magnetic fields B1 and B2 shifts, the ratio Ror doesnot change. Hence, while switching is executed by the power supply unit4 b such that the frequency ω0 of the exciting currents supplied to thefirst and second exciting coils 3 a and 3 b takes the two values ω1 andω2, the amplitude of the interelectrode electromotive force Eac isobtained in correspondence with each of the two value. When the flowrate is detected on the basis of the amplitude ratio Ror, the flow ratemeasurement error due to the influence of the shift can automatically becanceled.

Equation (69) can be rewritten torkv=rk{(Rorω2−ω1)sin(θ2/2)}/{(1−Ror)cos(θ2/2)}  (70)

From equation (24), equation (70) can be rewritten toV=α4×{(Rorω2−ω1)sin(θ2/2)}/{(1−Ror)cos(θ2/2)}for α4=1/γ  (71)where α4 (or γ) is a coefficient predetermined by calibration or thelike. With the above processing, the formula of a flow velocity V whenthe exciting currents with the frequency ω0=ω1 and the exciting currentswith the frequency ω0=ω2 are supplied to the first and second excitingcoils 3 a and 3 b can be obtained. The power supply unit 4 b suppliesthe exciting currents with the frequency ω0=ω1 and the exciting currentswith the frequency ω0=ω2 to the first and second exciting coils 3 a and3 b. The signal conversion unit 5 b obtains the amplitude of theinterelectrode electromotive force Eac detected by the electrodes 2 aand 2 b in each of the two states with different frequencies ω0 of theexciting currents and obtains the ratio Ror of the amplitudes. The flowrate output unit 6 b calculates the flow velocity V of the fluid to bemeasured by using equation (71) on the basis of the amplitude ratio Rorobtained by the signal conversion unit 5 b. With the above arrangement,the same effect as in the first embodiment can be obtained.

Eighth Embodiment

The eighth embodiment of the present invention will be described next.An electromagnetic flowmeter according to this embodiment has the samearrangement as that of the seventh embodiment, and a description thereofwill be made with reference to FIG. 12. In the seventh embodiment, theflow velocity V of the fluid to be measured is calculated by using theratio Ror of the amplitudes of the interelectrode electromotive forceEac. A flow velocity V of a fluid to be measured may be calculated byusing a ratio Rvx of the real axis components of amplitudes.

A magnitude x of the real axis component of the amplitude of aninterelectrode electromotive force Eac is given byx=bω0 rk sin(θ2)+brkv+brkv cos(θ2)  (72)

From equation (72), the ratio Rvx of a magnitude x1 of the real axiscomponent of the amplitude of the interelectrode electromotive force Eacwhen a frequency ω0 of the exciting current is ω1 to a magnitude x2 ofthe real axis component of the amplitude of the interelectrodeelectromotive force Eac when the frequency ω0=ω2 is given by$\begin{matrix}\begin{matrix}{{Rvx} = {{x1}/{x2}}} \\{= {\left\{ {{\omega\quad 1\quad{rk}\quad{\sin\left( {\theta\quad 2} \right)}} + {rkv} + {{rkv}\quad{\cos\left( {\theta\quad 2} \right)}}} \right\}/}} \\{\left\{ {{\omega\quad 2\quad{rk}\quad{\sin\left( {\theta\quad 2} \right)}} + {rkv} + {{rkv}\quad{\cos\left( {\theta\quad 2} \right)}}} \right\}}\end{matrix} & (73)\end{matrix}$

Equation (73) representing the ratio Rvx has no term of an amplitude bof magnetic fields B1 and B2. For this reason, even when the amplitude bof the magnetic fields B1 and B2 shifts, the ratio Rvx does not change.Equation (73) can be rewritten torkv=rk{(Rvxω2−ω1)sin(θ2)}/[(1−Rvx){1+cos(θ2)}]  (74)

From equation (24), equation (74) can be rewritten toV=α4×{(Rvxω2−ω1)sin(θ2)}/[(1−Rvx){1+cos(θ2)}] for α4=1/γ  (75)

A power supply unit 4 b supplies exciting currents with the frequencyω0=ω1 and the exciting currents with the frequency ω0=ω2 to first andsecond exciting coils 3 a and 3 b. A signal conversion unit 5 b obtainsthe amplitude of the real axis component of the interelectrodeelectromotive force Eac detected by electrodes 2 a and 2 b in each ofthe two states with different frequencies ω0 of the exciting currentsand obtains the ratio Rvx of the real axis components. A flow rateoutput unit 6 b calculates the flow velocity V of the fluid to bemeasured by using equation (75) on the basis of the amplitude ratio Rvxobtained by the signal conversion unit 5 b. With the above arrangement,the same effect as in the first embodiment can be obtained.

Ninth Embodiment

The ninth embodiment of the present invention will be described next. Anelectromagnetic flowmeter according to this embodiment has the samearrangement as that of the seventh embodiment, and a description thereofwill be made with reference to FIG. 12. In the seventh embodiment, theflow velocity V of the fluid to be measured is calculated by using theratio Ror of the amplitudes of the interelectrode electromotive forceEac. A flow velocity V of a fluid to be measured may be calculated byusing a ratio Rvy of the imaginary axis components of amplitudes.

A magnitude y of the imaginary axis component of the amplitude of aninterelectrode electromotive force Eac is given byy=bω0 rk−bω0 rk cos(θ2)+brkv sin(θ2)  (76)

From equation (76), the ratio Rvy of a magnitude yl of the imaginaryaxis component of the amplitude of the interelectrode electromotiveforce Eac when a frequency ω0 of the exciting current is ω1 to amagnitude y2 of the imaginary axis component of the amplitude of theinterelectrode electromotive force Eac when the frequency ω0=ω2 is givenby $\begin{matrix}\begin{matrix}{{Rvx} = {{y1}/{y2}}} \\{= {\left\{ {{\omega\quad 1\quad{rk}} - {\omega\quad 1\quad{rk}\quad{\cos\left( {\theta\quad 2} \right)}} + {{rkv}\quad{\sin\left( {\theta\quad 2} \right)}}} \right\}/}} \\{\left\{ {{\omega\quad 2\quad{rk}} - {\omega\quad 2\quad{rk}\quad{\cos\left( {\theta\quad 2} \right)}} + {{rkv}\quad{\sin\left( {\theta\quad 2} \right)}}} \right\}}\end{matrix} & (77)\end{matrix}$

Equation (77) representing the ratio Rvy has no term of an amplitude bof magnetic fields B1 and B2. For this reason, even when the amplitude bof the magnetic fields B1 and B2 shifts, the ratio Rvy does not change.Equation (77) can be rewritten torkv−rk[(Rvyω2−ω1){1−cos(θ2)}]/{(⊕−Rvy)sin(θ2)}  (78)

From equation (24), equation (78) can be rewritten toV=α4×[(Rvyω2−ω1){1−cos(θ2)}]/{(1−Rvy)sin(θ2)} for α4=1/γ  (79)

A power supply unit 4 b supplies exciting currents with the frequencyω0=ω1 and the exciting currents with the frequency ω0=ω2 to first andsecond exciting coils 3 a and 3 b. A signal conversion unit 5 b obtainsthe amplitude of the imaginary axis component of the interelectrodeelectromotive force Eac detected by electrodes 2 a and 2 b in each ofthe two states with different frequencies ω0 of the exciting currentsand obtains the ratio Rvy of the imaginary axis components. A flow rateoutput unit 6 b calculates the flow velocity V of the fluid to bemeasured by using equation (79) on the basis of the amplitude ratio Rvyobtained by the signal conversion unit 5 b. With the above arrangement,the same effect as in the first embodiment can be obtained.

As a characteristic feature of the seventh to ninth embodiments, aplurality of predetermined discrete values are used for the frequency ωof the exciting current. The frequency ω0 is not limited to two values.

10th Embodiment

The 10th embodiment of the present invention will be described next. Anelectromagnetic flowmeter according to this embodiment has the samearrangement as that of the fifth embodiment, and a description thereofwill be made with reference to FIG. 12. A power supply unit 4 b of thisembodiment supplies exciting currents having the same frequency ω0 and apredetermined phase difference θ2 to first and second exciting coils 3 aand 3 b. The power supply unit 4 b supplies the exciting currents to thefirst and second exciting coils 3 a and 3 b while continuously switchingthe frequency ω0. A signal conversion unit 5 b obtains the amplitude ofan interelectrode electromotive force detected by electrodes 2 a and 2 bin each of a plurality of states with different frequencies ω0 of theexciting currents and obtains the frequency ω0 for which the amplitudehas a predetermined value. On the basis of the frequency ω0 obtained bythe signal conversion unit 5 b, a flow rate output unit 6 b calculatesthe flow rate of a fluid to be measured.

This embodiment corresponds to a structure in which b1=b2 in equation(27) described above. For the descriptive convenience, b1=b2=b. Thefirst and second exciting coils 3 a and 3 b can have any arrangement aslong as b1=b2 can hold. The exciting coils can be arranged eithersymmetrically as in the second embodiment, or asymmetrically as in thethird or fourth embodiment. Exciting currents to be supplied from thepower supply unit 4 b to the first and second exciting coils 3 a and 3 bcan have either the same amplitude or different amplitudes.

A magnetic field B1 generated from the first exciting coil 3 a when theexciting current is supplied from the power supply unit 4 b is given byequation (44). A magnetic field B2 generated from the second excitingcoil 3 b is given by equation (45).

When b1=b2=b in equation (27), an interelectrode electromotive force Eacis given by equation (46). Four vectors representing the interelectrodeelectromotive force Eac have a geometrical relationship shown in FIG. 13described in the fifth embodiment. The principle of the fifth embodimentdescribed with reference to FIGS. 14 to 17 also holds in thisembodiment.

FIGS. 22A and 22B show the principle of flow rate measurement in thisembodiment. When the phase difference θ2 is constant, and the frequencyω0 is continuously changed, the phase difference θ2, for which thelength of the synthetic vector of four vector of equation (46) becomes0, is always present. The frequency at this time is defined as ω0_(A=0). The frequency, ω0 _(A=0) is given byω0 _(A=0) =−rkv/{rk tan(θ2/2)}  (80)

Equation (80) representing the frequency ω0 _(A=0) has no term of anamplitude b of the magnetic fields B1 and B2. For this reason, even whenthe amplitude b of the magnetic fields B1 and B2 shifts to b′, thefrequency ω0 _(A=0) does not change. The length of the synthetic vectorremains 0, as shown in FIGS. 22A and 22B. Hence, while continuouslychanging the frequency ω0, the amplitude of the interelectrodeelectromotive force Eac is obtained. When the flow rate is detected onthe basis of the frequency ω0 _(A=0) for which the amplitude has apredetermined value, the flow rate measurement error due to theinfluence of the shift can automatically be canceled.

To obtain the flow rate of the fluid to be measured, equation (80) isrewritten torkv=−ω0 _(A=0) rk tan(θ2/2)  (81)

On the basis of equation (24), equation (91) can be rewritten toV=α5×ω0 _(A=0) tan(θ2/2) for α5=−1/γ  (82)where α5 is a coefficient predetermined by calibration or the like. Thepower supply unit 4 b continuously switches the frequency ω0 of theexciting currents supplied to the first and second exciting coils 3 a an3 b. A signal conversion unit 5 b obtains the amplitude of theinterelectrode electromotive force Eac detected by electrodes 2 a and 2b in each of the plurality of states with different frequencies ω0 andobtains the frequency ω0 _(A=0) for which the amplitude Eac has apredetermined value of 0. A flow rate output unit 6 b calculates a flowvelocity V of the fluid to be measured by using equation (82) on thebasis of the frequency ω0 _(A=0) obtained by the signal conversion unit5 b. With the above arrangement, the same effect as in the firstembodiment can be obtained.

In the sixth and 10th embodiments, the predetermined value is set to 0as the simplest detailed example. However the present invention is notlimited to this. The basic principle of the sixth and 10th embodimentscan also be applied to any other amplitude except 0.

In the first to 10th embodiments, in-phase component noise can beremoved. Hence, the rectangular wave exciting method need not be used.Since the sine wave exciting method which uses a sine wave for anexciting current can be used, high-frequency excitation can be executed.When high-frequency excitation is used, 1/f noise can be removed, andthe response to a change in flow rate can be increased.

As the electrodes 2 a and 2 b used in the first to 10th embodiments,electrodes which are exposed from the inner wall of the measuring pipe 1and come into contact with the fluid to be measured may be used, asshown in FIG. 23. Alternatively, as shown in FIG. 24, capaditivelycoupled electrodes which do not come into contact with the fluid to bemeasured may be used. When capacitively coupled electrodes are used, theelectrodes 2 a and 2 b are covered with a lining 10 made of ceramic orTeflon and formed on the inner wall of the measuring pipe 1.

In the first to 10th embodiments, the two electrodes 2 a and 2 b areused. However, the present invention is not limited to this. The presentinvention can also be applied to an electromagnetic flowmeter havingonly one electrode. When only one electrode is used, a ground ring isprovided in the measuring pipe 1 to set the potential of the fluid to bemeasured to the ground potential. An electromotive force (the potentialdifference from the ground potential) generated in the single electrodeis detected by the signal conversion unit 5 or 5 b. When the twoelectrodes 2 a and 2 b are used, the electrode axis EAX forms a straightline that connects the electrodes 2 a and 2 b. When only one electrodeis used, it is assumed that a virtual electrode is arranged on the planePLN including the single real electrode at a position opposite to thereal electrode with respect to the measuring pipe axis PAX. The straightline that connects the real electrode and the virtual electrode at thistime corresponds to the electrode axis EAX.

The means for obtaining a phase difference φ in the signal conversionunit 5 and the flow rate output unit 6 in the first embodiment, themeans for obtaining the phase difference φ in the signal conversion unit5 and the flow rate output unit 6 a in the second to fourth embodiments,the means for obtaining the ratio R in the signal conversion unit 5 band the flow rate output unit 6 b in the fifth embodiment, the means forobtaining the phase difference θ2 _(A=0) in the signal conversion unit 5b and the flow rate output unit 6 b in the sixth embodiment, the meansfor obtaining the ratio Ror, Rvx, or Rvy in the signal conversion unit 5b and the flow rate output unit 6 b in the seventh to ninth embodiments,and the means for obtaining the frequency ω0 _(A=0) in the signalconversion unit 5 b and the flow rate output unit 6 b in the 10thembodiment can be implemented by, e.g., a computer.

INDUSTRIAL APPLICABILITY

As described above, the present invention is suitable for anelectromagnetic flowmeter using a sine wave exciting method which isreadily affected by in-phase component noise.

1. An electromagnetic flowmeter characterized by comprising: a measuringpipe through which a fluid to be measured flows; an electrode which isarranged in said measuring pipe and detects an electromotive forcegenerated by a magnetic field changing over time and applied to thefluid and flow of the fluid; an asymmetrical exciting unit which appliesasymmetrical magnetic fields to the fluid on both sides of a planeserving as a boundary in said measuring pipe, the plane including saidelectrode, being perpendicular to an axial direction of said measuringpipe, and being defined as the boundary in said measuring pipe; a signalconversion unit which obtains, from an electromotive force detected bysaid electrode, an asymmetrical exciting characteristic parameter whichdepends on a flow rate of the fluid and does not depend on a flow ratemeasurement error; and a flow rate output unit which calculates the flowrate of the fluid for which the flow rate measurement error has beencorrected on the basis of the asymmetrical exciting characteristicparameter.
 2. An electromagnetic flowmeter according to claim 1,characterized in that said asymmetrical exciting unit comprises anexciting coil which is arranged at a position separated from the planeby an offset distance, and a power supply unit which supplies anexciting current to said exciting coil.
 3. An electromagnetic flowmeteraccording to claim 1, characterized in that said signal conversion unitobtains as the asymmetrical exciting characteristic parameter, a phasedifference between an exciting current supplied to an exciting coil ofsaid asymmetrical exciting unit and the electromotive force detected bysaid electrode, and said flow rate output unit calculates the flow rateof the fluid on the basis of the phase difference obtained by saidsignal conversion unit.
 4. An electromagnetic flowmeter according toclaim 1, characterized in that said asymmetrical exciting unit comprisesa first exciting coil which is arranged at a position separated from theplane by an offset distance, a second exciting coil which is arranged ata position different from that of said first exciting coil, and a powersupply unit which supplies exciting currents having the same phase tosaid first exciting coil and said second exciting coil, and in amagnetic field generated from said first exciting coil and a magneticfield generated from said second exciting coil, magnetic fieldcomponents which are perpendicular to both of an axial direction of saidelectrode and the axial direction of said measuring pipe have the samephase and different amplitudes on the axis of said electrode.
 5. Anelectromagnetic flowmeter according to claim 1, characterized in thatsaid asymmetrical exciting unit comprises a first exciting coil which isarranged at a position separated from the plane by an offset distance, asecond exciting coil which is arranged at a position different from thatof said first exciting, coil, and a power supply unit which suppliesexciting currents to said first exciting coil and said second excitingcoil while changing a phase difference between the exciting currentsupplied to said first exciting coil and the exciting current suppliedto said second exciting coil, and in a magnetic field generated fromsaid first exciting coil and a magnetic field generated from said secondexciting coil, magnetic field components which are perpendicular to bothof an axial direction of said electrode and the axial direction of saidmeasuring pipe have the same amplitude on the axis of said electrode,and the phase difference between the magnetic field component of saidfirst exciting coil and the magnetic field component of said secondexciting coil takes at least two values.
 6. An electromagnetic flowmeteraccording to claim 1, characterized in that said signal conversion unitobtains an amplitude of the electromotive force detected by saidelectrode for each of at least two states with different phasedifferences between the exciting currents supplied to said two excitingcoils of said asymmetrical exciting unit and obtains a ratio of theamplitudes as the asymmetrical exciting characteristic parameter, andsaid flow rate output unit calculates the flow rate of the fluid on thebasis of the ratio of the amplitudes obtained by said signal conversionunit.
 7. An electromagnetic flowmeter according to claim 1,characterized in that said asymmetrical exciting unit comprises a firstexciting coil which is arranged at a position separated from the planeby an offset distance, a second exciting coil which is arranged at aposition different from that of said first exciting coil, and a powersupply unit which supplies exciting currents to said first exciting coiland said second exciting coil while continuously switching a phasedifference between the exciting current supplied to said first excitingcoil and the exciting current supplied to said second exciting coil, andin a magnetic field generated from said first exciting coil and amagnetic field generated from said second exciting coil, magnetic fieldcomponents which are perpendicular to both of an axial direction of saidelectrode and the axial direction of said measuring pipe have the sameamplitude on the axis of said electrode, and the phase differencebetween the magnetic field component of said first exciting coil and themagnetic field component of said second exciting coil continuouslyswitches.
 8. An electromagnetic flowmeter according to claim 1,characterized in that said signal conversion unit obtains an amplitudeof the electromotive force detected by said electrode for each of aplurality of states with different phase differences between theexciting currents supplied to said two exciting coils of saidasymmetrical exciting unit and obtains, as the asymmetrical excitingcharacteristic parameter, the phase difference for which the amplitudehas a predetermined value, and said flow rate output unit calculates theflow rate of the fluid on the basis of the phase difference obtained bysaid signal conversion unit.
 9. An electromagnetic flowmeter accordingto claim 1, characterized in that said asymmetrical exciting unitcomprises a first exciting coil which is arranged at a positionseparated from the plane by an offset distance, a second exciting coilwhich is arranged at a position different from that of said firstexciting coil, and a power supply unit which supplies exciting currentshaving the same frequency and a predetermined phase difference to saidfirst exciting coil and said second exciting coil while changing thefrequency, and in a magnetic field generated from said first excitingcoil and a magnetic field generated from said second exciting coil,magnetic field components which are perpendicular to both of an axialdirection of said electrode and the axial direction of said measuringpipe have the same amplitude, same frequency, and the predeterminedphase difference on the axis of said electrode, and the frequency of themagnetic field component switches between at least two values.
 10. Anelectromagnetic flowmeter according to claim 1, characterized in thatsaid signal conversion unit obtains an amplitude of the electromotiveforce detected by said electrode for each of at least two states inwhich the frequency of the exciting currents supplied to said twoexciting coils of said asymmetrical exciting unit switches and obtains aratio of the amplitudes as the asymmetrical exciting characteristicparameter, and said flow rate output unit calculates the flow rate ofthe fluid on the basis of the ratio of the amplitudes obtained by saidsignal conversion unit.
 11. An electromagnetic flowmeter according toclaim 1, characterized in that said asymmetrical exciting unit comprisesa first exciting coil which is arranged at a position separated from theplane by an offset distance, a second exciting coil which is arranged ata position different from that of said first exciting coil, and a powersupply unit which supplies exciting currents having the same frequencyand a predetermined phase difference to said first exciting coil andsaid second exciting coil while continuously switching the frequency,and in a magnetic field generated from said first exciting coil and amagnetic field generated from said second exciting coil, magnetic fieldcomponents which are perpendicular to both of an axial direction of saidelectrode and the axial direction of said measuring pipe have the sameamplitude, same frequency, and the predetermined phase difference on theaxis, of said electrode, and the frequency of the magnetic fieldcomponent continuously switches.
 12. An electromagnetic flowmeteraccording to claim 1, characterized in that said signal conversion unitobtains an amplitude of the electromotive force detected by saidelectrode for each of a plurality of states in which the frequency ofthe exciting currents supplied to said two exciting coils of saidasymmetrical exciting unit switches and obtains, as the asymmetricalexciting characteristic parameter, the frequency of the exciting currentfor which the amplitude has a predetermined value, and said flow rateoutput unit calculates the flow rate of the fluid on the basis of thefrequency obtained by said signal conversion unit.
 13. Anelectromagnetic flowmeter characterized by comprising: a measuring pipethrough which a fluid to be measured flows; an electrode which isarranged in said measuring pipe and detects an electromotive forcegenerated by a magnetic field applied to the fluid and flow of thefluid; an exciting coil which is arranged at a position separated from aplane by an offset distance and applies asymmetrical magnetic fields tothe fluid on both sides of the plane serving as a boundary in saidmeasuring pipe, the plane including said electrode, being perpendicularto an axial direction of said measuring pipe, and being defined as theboundary in said measuring pipe; a power supply unit which supplies anexciting current to said exciting coil; a signal conversion unit whichobtains a phase difference between the exciting current and anelectromotive force detected by said electrode; and a flow rate outputunit which calculates a flow rate of the fluid on the basis of the phasedifference obtained by said signal conversion unit.
 14. Anelectromagnetic flowmeter characterized by comprising: a measuring pipethrough which a fluid to be measured flows; an electrode which isarranged in said measuring pipe and detects an electromotive forcegenerated by a magnetic field applied to the fluid and flow of thefluid; a first exciting coil which is arranged at a position separatedfrom a plane by an offset distance, the plane including said electrode,being perpendicular to an axial direction of said measuring pipe, andbeing defined as the boundary in said measuring pipe; a second excitingcoil which is arranged at a position different from that of said firstexciting coil; a power supply unit which supplies exciting currentshaving the same phase to said first exciting coil and said secondexciting coil; a signal conversion unit which obtains a phase differencebetween the exciting current and an electromotive force detected by saidelectrode; and a flow rate output unit which calculates a flow rate ofthe fluid on the basis of the phase difference obtained by said signalconversion unit, wherein in a magnetic field generated from said firstexciting coil and a magnetic field generated from said second excitingcoil, magnetic field components which are perpendicular to both of anaxial direction of said electrode and the axial direction of saidmeasuring pipe have the same phase and different amplitudes on the axisof said electrode.
 15. An electromagnetic flowmeter according to any oneof claims 3, 13, and 14 characterized in that on the basis of the phasedifference φ obtained by said signal conversion unit, said flow rateoutput unit calculates the flow rate of the fluid by α1×tan(π/2)(α1 is acoefficient).
 16. An electromagnetic flowmeter characterized bycomprising: a measuring pipe through which a fluid to be measured flows;an electrode which is arranged in said measuring pipe and detects anelectromotive force generated by a magnetic field applied to the fluidand flow of the fluid; a first exciting coil which is arranged at aposition separated from a plane by an offset distance, the planeincluding said electrode, being perpendicular to an axial direction ofsaid measuring pipe, and being defined as the boundary in said measuringpipe; a second exciting coil which is arranged at a position differentfrom that of said first exciting coil; a power supply unit whichsupplies exciting currents to said first exciting coil and said secondexciting coil while changing a phase difference between the excitingcurrent supplied to said first exciting coil and the exciting currentsupplied to said second exciting coil; a signal conversion unit whichobtains an amplitude of the electromotive force detected by saidelectrode for each of at least two states with different phasedifferences and obtains a ratio of the amplitudes; and a flow rateoutput unit which calculates a flow rate of the fluid on the basis ofthe ratio of the amplitudes obtained by said signal conversion unit,wherein in a magnetic field generated from said first exciting coil anda magnetic field generated from said second exciting coil, magneticfield components which are perpendicular to both of an axial directionof said electrode and the axial direction of said measuring pipe havethe same amplitude on the axis of said electrode, and the phasedifference between the magnetic field component of said first excitingcoil and the magnetic field component of said second exciting coil takesat least two values.
 17. An electromagnetic flowmeter according to claim6 or 16, characterized in that when the phase difference between theexciting current supplied to said first exciting coil and the excitingcurrent supplied to said second exciting coil takes two values 2χ and 2ψ(χ and ψ are different real numbers), said flow rate output unitcalculates, on the basis of a ratio R of the amplitudes obtained by saidsignal conversion unit, the flow rate of the fluid by α2×{(R sin ψ−sinχ)/(R cos ψ−cos χ)} (θ2 is a coefficient).
 18. An electromagneticflowmeter characterized by comprising: a measuring pipe through which afluid to be measured flows; an electrode which is arranged in saidmeasuring pipe and detects an electromotive force generated by amagnetic field applied to the fluid and flow of the fluid; a firstexciting coil which is arranged at a position separated from a plane byan offset distance, the plane including said electrode, beingperpendicular to an axial direction of said measuring pipe, and beingdefined as the boundary in said measuring pipe; a second exciting coilwhich is arranged at a position different from that of said firstexciting coil; a power supply unit which supplies exciting currents tosaid first exciting coil and said second exciting coil whilecontinuously switching a phase difference between the exciting currentsupplied to said first exciting coil and the exciting current suppliedto said second exciting coil; a signal conversion unit which obtains anamplitude of the electromotive force detected by said electrode for eachof a plurality of states with different phase differences and obtainsthe phase difference for which the amplitude has a predetermined value;and a flow rate output unit which calculates a flow rate of the fluid onthe basis of the phase difference obtained by said signal conversionunit, wherein in a magnetic field generated from said first excitingcoil and a magnetic field generated from said second exciting coil,magnetic field components which are perpendicular to both of an axialdirection of said electrode and the axial direction of said measuringpipe have the same amplitude on the axis of said electrode and the phasedifference between the magnetic field component of said first excitingcoil and the magnetic field component of said second exciting coilcontinuously switches.
 19. An electromagnetic flowmeter according toclaim 8 or 18, characterized in that on the basis of the phasedifference θ2 obtained by said signal conversion unit, said flow rateoutput unit calculates the flow rate of the fluid by α3×tan(θ2/2) (α3 isa coefficient).
 20. An electromagnetic flowmeter characterized bycomprising: a measuring pipe through which a fluid to be measured flows;an electrode which is arranged in said measuring pipe and detects anelectromotive force generated by a magnetic field applied to the fluidand flow of the fluid; a first exciting coil which is arranged at aposition separated from a plane by an offset distance, the planeincluding said electrode, being perpendicular to an axial direction ofsaid measuring pipe, and being defined as the boundary in said measuringpipe; a second exciting coil which is arranged at a position differentfrom that of said first exciting coil; a power supply unit whichsupplies exciting currents having the same frequency and a predeterminedphase difference to said first exciting coil and said second excitingcoil while changing the frequency; a signal conversion unit whichobtains an amplitude of the electromotive force detected by saidelectrode for each of at least two states with different frequencies andobtains a ratio of the amplitudes; and a flow rate output unit whichcalculates a flow rate of the fluid on the basis of the ratio of theamplitudes obtained by said signal conversion unit, wherein in amagnetic field generated from said first exciting coil and a magneticfield generated from said second exciting coil, magnetic fieldcomponents which are perpendicular to both of an axial direction of saidelectrode and the axial direction of said measuring pipe have the sameamplitude, same frequency, and the predetermined phase difference on theaxis of said electrode, and the frequency of the magnetic fieldcomponent switches between at least two values.
 21. An electromagneticflowmeter according to claim 10 or 20, characterized in that when thefrequency of the exciting currents supplied to said first and secondexciting coils switches between two values ω1 and ω2, said flow rateoutput unit calculates, on the basis of a ratio Ror of the amplitudesobtained by said signal conversion unit, the flow rate of the fluid byα4×{(Rorω2−ω1)sin(θ2/2)}/{(1−Ror)cos(θ2/2)} (α4 is a coefficient). 22.An electromagnetic flowmeter characterized by comprising: a measuringpipe through which a fluid to be measured flows; an electrode which isarranged in said measuring pipe and detects an electromotive forcegenerated by a magnetic field applied to the fluid and flow of thefluid; a first exciting coil which is arranged at a position separatedfrom a plane by an offset distance, the plane including said electrode,being perpendicular to an axial direction of said measuring pipe, andbeing defined as the boundary in said measuring pipe; a second excitingcoil which is arranged at a position different from that of said firstexciting coil; a power supply unit which supplies exciting currentshaving the same frequency and a predetermined phase difference to saidfirst exciting coil and said second exciting coil while continuouslyswitching the frequency; a signal conversion unit which obtains anamplitude of the electromotive force detected by said electrode for eachof a plurality of states with different frequencies and obtains thefrequency for which the amplitude has a predetermined value; and a flowrate output unit which calculates a flow rate of the fluid on the basisof the frequency obtained by said signal conversion unit, wherein in amagnetic field generated from said first exciting coil and a magneticfield generated from said second exciting coil, magnetic fieldcomponents which are perpendicular to both of an axial direction of saidelectrode and the axial direction of said measuring pipe have the sameamplitude, same frequency, and the predetermined phase difference on theaxis of said electrode, and the frequency of the magnetic fieldcomponent continuously switches.
 23. An electromagnetic flowmeteraccording to claim 12 or 22, characterized in that on the basis of thephase difference θ2 between the exciting current supplied to said firstexciting coil and the exciting current supplied to said second excitingcoil and the frequency ω0 obtained by said signal conversion unit, saidflow rate output unit calculates the flow rate of the, fluid by α5×ω0tan(θ2/2) (α5 is a coefficient).
 24. An electromagnetic flowmeteraccording to any one of claims 1, 13, 14, 16, 18, 20, and 22,characterized in that said electromagnetic flowmeter uses a sine waveexciting method.
 25. An electromagnetic flowmeter according to any oneof claim 1, 13, 14, 16, 18, 20, and 22, characterized in that the numberof said electrodes is one.